ISSP International Workshop and Symposium on

Computational ApproachestoQuantum Critical Phenomena(August 9 - 11, 2006)(Program: Oral Session)
August 9, 2006
9:50-

Opening Address

10:00-10:30 Quantum Monte Carlo study of many-body systems coupled with lattice
degrees of freedom
Takeo Kato (ISSP, University of Tokyo)
10:30-11:00 Calculation of correlation functions of spin 1/2 XXX chain
Minoru Takahashi (ISSP, University of Tokyo)
11:00-11:30 Dynamics and magnetization process of triangle based low dimensional systems, ring, tube, helix and ballHiroyuki Nojiri (Institute for Materials Research, Touhoku University)
11:30-12:00 Spin Nematic State in a Triangular Antiferromagnet
Hirokazu Tsunetsugu (Yukawa Institute for Theoretical Physics, Kyoto University)
12:00-12:30 Metamagnetism and related critical phenomena in pyrochlore Heisenberg
antiferromagnets
Yukitoshi Motome (Department of Applied Physics, University of Tokyo)— Lunch —14:00-14:30 Emerging spatial structures in SU(N) Heisenberg model
Naoki Kawashima (ISSP, University of Tokyo)
14:30-15:00 Quantum Phase Transition between Two Ordered Phases with Unrelated
Symmetries
Kenji Harada (Department of Applied Analysis and Complex Dynamical Systems, Kyoto Univsersity)

15:00-15:30 Stripe formation in doped Hubbard ladders
Eric Jeckelmann (Institute for Theoretical Physics, University of Hannover)
16:00-16:30 Real space renormalization group approach for the corner Hamiltonian
Kouichi Okunishi (Department of Physics, Niigata University)
16:30-17:00 The ALPS Project: Open Source Software for Classical and Quantum Lattice Models
Matthias Troyer (Institut für Theoretische Physik, ETH Hünggerberg)
17:00-17:30 Universal Relation in Critical Temperature of Strongly Anisotropic Magnets
Synge Todo (Department of Applied Physics, University of Tokyo)
17:30-18:00 DMFT results for the spin-1/2 Kondo lattice model
Philipp Werner (Columbia University)
18:00-

Poster Session

August 10, 2006
9:00-9:30

ICAMipedia
Daniel Cox (Institute for Complex Adaptive Matter of the University of California)

9:30-10:00

Searching for a supersolid phase in three dimensions
Takafumi Suzuki (ISSP, University of Tokyo)

10:00-10:30 A new high ﬁeld phase in the frustrated 2D dimer spin system SrCu2 (BO3 )2Masashi Takigawa (ISSP, University of Tokyo)
11:00-11:30 Magnetic Quantum Phase Transitions and Critical Behavior in TlCuCl3
and KCuCl3
Hidekazu Tanaka (Tokyo Institute of Technoloby)
11:30-12:00 A Bose-Einstein condensate of magnons in anisotropic quantum magnets
BaCuSi2 O6 and NiCl2−4 SC(NH2 )2Marcelo Jaime (National High Magnetic Field Laboratory, Los Alamos National
Laboratory)
12:00-12:30 Geometrical Frustration and Dimensional Reduction at a Quantum Critical Point
Cristian Batista (Condensed Matter and Statistical Physics, Los Alamos National Laboratory)— Lunch —0

14:00-14:30 I2CAM Fellowships
Daniel Cox (Institute for Complex Adaptive Matter of the University of California)
14:30-15:00 Field-Induced Quantum Critical Phenomena in Quasi-1D Spin Systems
Toru Sakai (Japan Atomic Energy Agency/Spring-8)
15:00-15:30 Emergence of Long Period Antiferromagnetic and Ferrimagnetic Orders
Due to Anisotropy Modulation in High Spin Heisenberg Chains
Kazuo Hida (Department of Physics, Saitama University)
16:00-16:30 Tomonaga-Luttinger liquid induced by a magnetic ﬁeld in a gapped quasi1D antiferromagnet
Masayuki Hagiwara (High Magnetic Field Laboratory, Osaka University)
16:30-17:00 Quantum Critical ”Opalescence”
Masatoshi Imada (Department of Applied Physics, University of Tokyo)
17:00-17:30 Phase-space methods for fermions: bounded distributions and stochastic
gausesJoel Corney (Department of Physics, The University of Queensland)
17:30-18:00 Highly Correlated Electrons on Triangular Lattice; Mott Criticality, Spin
Liquid and Superconductivity
Kazushi Kanoda (Department of Applied Physics, University of Tokyo)
18:00-

BanquetAugust 11, 2006
9:00-9:30

Finite Temperature Eﬀects on the Excitation Spectrum in Quantum Critical
Magnetic Insulators
Christian Rüegg (Department of Physics and Astronomy, University College London

9:30-10:00

Ion Exchange as a Tool to Explore Two-Dimensional Square Lattice Antiferromagnets
Hiroshi Kageyama (Department of Chemistry, Graduate School of Science, Kyoto University

10:00-10:30 Magnetic multipole orders in frustrated ferromagnets
Tsutomu Momoi (RIKEN)
11:00-11:30 Duality and ﬁnite-size scaling analysis of the two-dimensional diluted Villain model
Yutaka Okabe (Department of Physics, Tokyo Metropolitan University)1

11:30-12:00 Kondo Problems in Quantum Critical Environments
Hideaki Maebashi (ISSP, University of Tokyo)
12:00-12:30 Magnetic structure in inhomogeneous systems and time-dependent systems
Seiji Miyashita (Department of Physics, University of Tokyo)— Lunch —14:00-14:30 A numerical algorithm for the eigenvalue distribution of non-Hermitianmatrices
Naomichi Hatano (Institute of Industrial Science, University of Tokyo)
14:30-15:00 The correlation density matrix: new tool for analyzing exact diagonalizations?
C. L. Henley (Institute of Industrial Science, University of Tokyo)
15:00-15:30 Ferromagnetism and Quantum Statistics
Masaki Oshikawa (ISSP, University of Tokyo)
15:30-16:00 Flowgram method for precise studies of poly-critical points and deconﬁned
criticality as a theory of weak ﬁrst order transitions
Nikolay Prokof’ev (Department of Physics, University of Massachusetts,
Amherst)16:00-16:30 Deconﬁned quantum criticality in a 2D Heisenberg model with four-spin
interactions
Anders Sandvik (Department of Physics, Boston University)(Poster Session: Program)
18:00- August 9, 2006
P1

Spin-triplet superconductivity in the double-chain Hubbard model with ferromagnetic exchange interaction
Tomonori Shirakawa (Department of Physics, Chiba University)

P2

Density matrix renormalization group study of dynamics in correlated electron systems with environment
Hiroaki Matsueda (Department of Physics, Tohoku University)

2

P3

Stability of One-dimensional Mott Insulators against Charge Fluctuations by theDensity Matrix Renormalization Group Method
Isao Maruyama (Department of Applied Physics, University of Tokyo)

P4

Numerical study of diluted orbital
Takayoshi Tanaka (Department of Physics, Tohoku University)

P5

Eﬀects of Impurities in Quasi-One-Dimensional Haldane Antiferromagnets
Munehisa Matsumoto (ETH Zurich)

P6

Pairing Phase in Bosonic Systems with Correlated Hopping
Andreas Läuchli (IRRMA - EPF Lausanne)

P7

Bond-Dilution-Induced Quantum Phase Transitions in Heisenberg Antiferromagnets
Chitoshi Yasuda (Department of Physics and Mathematics, Aoyama Gakuin University)

P8

Low-energy properties of one-dimensional spin-orbital model
Hiroaki Onishi (Advanced Science Research Center, Japan Atomic Energy Agency

P9

Surface and corner multifractality in two-dimensional symplectic class
Hideaki Obuse (Condensed Matter Theory Laboratory, RIKEN)

P10

Non-linear transport in a commensurate CDW and universal KPZ ﬂuctuation
Takashi Oka (Department of Physics, University of Tokyo)

P11

Dynamical properties of photoexcited states in one-dimensional dimerized Mott insulators
Nobuya Maeshima (Institute for Molecular Science)

P12

Quantum Monte Carlo study of the multiorbital Hubbard model with spin andorbital rotational symmetries.
Shiro Sakai (Department of Physics, University of Tokyo)

P14

The Anderson transitions in 3D, 2D, and below 2D
Yoichi Asada (Department of Physics, Tokyo Institute of Technology)

P15

Mean ﬁeld quantum annealing
Sei Suzuki (Department of Physics, Tokyo Institute of Technology)

P16

New type of quantum liquid of spinless fermions on an anisotropic triangular lattice
Chisa Hotta (Aoyama Gakuin University)

P17

Magnetization plateaux for distorted triangular antiferromagnet Cs2 CuBr4
Shin Miyahara (Aoyama Gakuin University)

3

P18

Re-entrant quantum phase transitions with respect to the XXZ anisotropy parameter in spin chains
Kiyomi Okamoto (Department of Physics, Tokyo Institute of Technology)

P19

Modiﬁcation of Directed-Loop Algorithm for Continuous Space Simulation of
Bosonic Systems
Yasuyuki Kato (Institute of Solid State Physics, University of Tokyo)

Sponsors
Institute for Solid State Physics, University of Tokyo
21st Century COE Program ”Quantum Extreme Systems and Their Symmetries”
National Science Foundation (NSF)
Institute for Complex Adaptive Matter (ICAM)

4

Abstracts: Oral Session on August 9th

10:00-

Quantum Monte Carlo study of many-body systems coupled withlattice degrees of freedom
Takeo Kato (ISSP, University of Tokyo)
Importance of electron-lattice couplings have been recognized for long time in lowdimensional correlated systems like organic conductors. It, however, remains an
unsolved problem to consider strong competition between different phases inducedby changing dimensionality of the system. In order to approach this problem, I haverecently developed a novel algorithm to deal with correlated systems coupled to lattice degrees of freedom based on the stochastic series expansion (SSE) method. By
applying it to the spin-Peierls model with interchain exchange interaction, I discuss
competition effects between antiferromagnetism and spin-Peierls transition. I alsomention other applications of the present algorithm.

10:30-

Calculation of correlation functions of spin 1/2 XXX chain
Minoru Takahashi (ISSP, University of Tokyo)
The calculation of the correlation functions of Bethe ansatz solvable models is very
difﬁcult problem. Among these solvable models spin 1/2 XXX chain has been investigated for a long time. Even for this model only the nearest neighbor and the second
neighbor correlations were known. In 1990’s Kyoto group gave multiple integral
formula for the general correlations. But the integration of this formula is also very
difﬁcult problem. Recently these integrals are decomposed to products of one dimensional integrals and correlation functions are expressed by log 2 and Riemann’s
zeta functions with odd integer argument ζ(3), ζ(5), ζ(7),.... We can calculate density
matrix of successive six sites. This means that all correlations in successive 6 sites
can be calculated. These method can be extended to XXZ chain. I will review recent
progress in the calculations of correlation functions.

5

11:00-

Dynamics and magnetization process of triangle based low dimensional systems, ring, tube, helix and ballHiroyuki Nojiri (Institute for Materials Research, Touhoku University)
A spin chirality brings a new internal degree of freedom in spin systems made up of
triangular spin rings such as prism, tube, helix and polyhedron. The cross term of
the chirality and the spin gives rise to a variety of magnetic properties in such systems. A simple but interesting example is found in the spin ring. A purely adiabatic
magnetization process is conﬁrmed by the observation of half-step magnetization.
Similar behavior is found in a spin polyhedron of tri-diminished icosihedron, where
the ground state is doubly degenerated. In spin polyhedron of huge number of states,
the magnetization plateau is found at the 1/3 of saturation and is interpreted by theorder by disorder mechanism.
It is also important that the spin chirality is closely connected with the structuralchirality. In a triangle ring, the distortion from the regular triangle mostly results inthe chiral structure that gives the difference between the upward and the downward
directions in the spin ring. When such chiral rings are connected into a chain, a helixof mono-chirality can be formed and the non-linear properties are expected in bothdielectric and magnetic sectors.

11:30-

Spin Nematic State in a Triangular Antiferromagnet
Hirokazu Tsunetsugu (Yukawa Institute for Theoretical Physics, Kyoto University)
In some triangular antiferromagnets, no magnetic long range order is observed, but
speciﬁc heat and magnetic susceptibility indicate the presence of gapless excitations.
To explain these properties, we have proposed a scenario of spin nematic order andcompared the results particularly with NiGa2 S4 , a spin-1 system. I will report theeffects of quantum ﬂuctuations in the nematic ordered state on observable magnetic
properties, and also other characteristic correlations.

6

12:00-

Metamagnetism and related critical phenomena in pyrochlore
Heisenberg antiferromagnets
Yukitoshi Motome (Department of Applied Physics, University of Tokyo)
It is well known that the Heisenberg model with classical spins on the highlyfrustrated pyrochlore lattice has a massively degenerate ground-state manifold anddoes not order magnetically at any temperature if the exchange interaction is limited
to between nearest-neighbor spins. This fact is not changed by the addition of magnetic ﬁeld; the degeneracy survives and the magnetization process does not show
any characteristic feature up to the saturation ﬁeld, at any temperature. However
this system is in a ’critical’ state, and dramatic changes can be expected whenevera perturbation is introduced which lifts the degeneracy of the ground-state manifold. In this presentation we explore the fascinating new effects which arise in an
extended Heisenberg model originally introduced to explain the metamagnetic transition seen in Cr spinel oxides, ACr2 O4 (A =Cd, Hg). In particular, we consider
the consequences of thermal ﬂuctuations on a Heisenberg model perturbed by additional longer-range interactions (which can lead to a variety of different formsof magnetic order), and of additional biquadratic interactions (which favour stateswith collinear spins). Using classical Monte Carlo simulation and low-temperature
expansion techniques, we uncover a range of novel phenomena as a consequenceof the delicate interplay among different perturbations; a spin-liquid metamagnetic
state which exhibits a ’spin pseudogap’ without any long-range magnetic order, aspin-nematic state with quadrupole ordering of spins, and a ﬂuctuation-driven metamagnetic phase.

14:00-

Emerging spatial structures in SU(N) Heisenberg model
Naoki Kawashima (ISSP, University of Tokyo)
The ordinary Heisenberg model that possesses the SU(2) symmetry can easily begeneralized to higher symmetry simply by regarding a symbol ”S” in the Heisenberg
Hamiltonian as a generator of the SU(N) instead of SU(2). Here we concentrateon the two-dimensional model with symmetric representations, namely, the cases
where an SU(N) spin can be expressed as a small number of, say M, bosons with N
types. Besides possible connections to electron systems with orbital degeneracy, thismodel is interesting for several reasons. For example, it is theoretically predicted
that, depending on the value of M and N, the SU(N) Heisenberg model may exhibit
a quantum disordered state as well as various ground states with non-trivial spatial
structures, such as the dimerized state and the striped state. From quantum Monte
Carlo simulation, we ﬁnd that it is indeed true for M = 1 but only for N ≥ 5 where
spontaneous dimerization can be observed. The case of M > 1 and the possibility ofthe disordered ground state are also discussed.

7

14:30-Quantum Phase Transition between Two Ordered Phases with Unrelated Symmetries
Kenji Harada (Dept. of Applied Analysis and Complex Dynamical Systems, Kyoto Univ.)
We show results of quantum Monte Carlo simulations for the quasi-one dimensional
S = 1 biquadratic Heisenberg antiferromagnet. When the spatial anisotropy is varied, a direct phase transition from the spontaneous dimerized phase to the Neel ordered phase is observed. If it is a continuous phase transition, it shows an unconventional critical phenomena that may separate two phases of which the symmetrygroup of the lower-symmetry phase is not a sub-group of the other.

15:00-

Stripe formation in doped Hubbard ladders
Eric Jeckelmann (Institute for Theoretical Physics, University of Hannover)
We investigate the formation of stripes in six-leg Hubbard ladders doped away fromhalf ﬁlling using the density-matrix renormalization group method. A parallelized
code allows us to keep enough density-matrix eigenstates and to study sufﬁciently
large systems to extrapolate the stripe amplitude to the limits of vanishing DMRG
truncation error and inﬁnitely long ladders. Our work gives strong evidence forthe existence of a long-range ordered stripe phase above a critical coupling U/t in
Hubbard ladders.
[1] G. Hager et al., Phys. Rev. B 71, 075108 (2005)

16:00-

Real space renormalization group approach for the corner Hamiltonian
Kouichi Okunishi (Department of Physics, Niigata University)
The density matrix renormalization group(DMRG) is a very powerful numerical tool
to study 1D quantum many body systems. In my talk, I would like to focus onsome fundamental aspects of DMRG particularly of the inﬁnite system size method,which may be a challenging problem to understand the success of DMRG and its
implication to the critical phenomena. When considering the theoretical backgroundof DMRG, it is essentially important to analyze the nature of the eigenvalue spectrumof the reduced density matrix. I explain the relation between the reduced density
matrix and the corner Hamiltonian, which is a generator of Baxter’s corner transfer
matrix in 2D classical systems. I then present a novel real-space-renormalizationgroup approach for this corner Hamiltonian and demonstrate it for the S = 1/2 XXZ
spin chain. I also examine the renormalization group for the S = 1 Heisenberg
spin chain and then discuss implications of the eigenvalue spectrum of the corner
Hamiltonian to DMRG.

8

16:30-The fate of vacancy-induced supersolidity in 4 He
Matthias Troyer (Institut für Theoretische Physik, ETH Hünggerberg)
The supersolid state of matter, exhibiting non-dissipative ﬂow in solids, has been
elusive for thirty ﬁve years. The recent discovery of a non-classical moment of inertia in solid 4 He by Kim and Chan provided the ﬁrst experimental evidence, although
the interpretation in terms of supersolidity of the ideal crystal phase remains subject
to debate. Using quantum Monte Carlo methods we investigate the long-standing
question of vacancy-induced superﬂow and ﬁnd that vacancies in a 4 He crystal phaseseparate instead of forming a supersolid. On the other hand, non-equilibrium vacancies relaxing on defects of poly-crystalline samples could provide an explanation for
the experimental observations.
Reference: cond-mat/0605627

17:00-

Universal Relation in
Anisotropic Magnets

CriticalTemperatureofStrongly

Synge Todo (Department of Applied Physics, University of Tokyo)
A novel universal relation in the critical temperature of quasi-one-dimensional magnets is investigated by the cluster Monte Carlo method. It is found that in the weakinterchain coupling regime the critical temperature obeys a chain mean-ﬁeld likerelation with a reduced effective coordination number [1,2]. Furthermore, the renormalized coordination number is universal, i.e. independent of spin size. This universality is rigorously proved for the case of Ising anisotropy by considering a mappingto the quantum Ising model.
[1] C. Yasuda, S. Todo, K. Hukushima, F. Alet, M. Keller, M. Troyer, and H.
Takayama, Phys. Rev. Lett. 94, 217201 (2005).
[2] S. Todo, cond-mat/0606790.
17:30-DMFT results for the spin-1/2 Kondo lattice model
Philipp Werner (Columbia University)
I will reformulate a recently developed strong-coupling, continuous-time impurity
solver in a manner appropriate for general classes of quantum impurity models. The
method will be applied to the dynamical mean ﬁeld theory of the ferromagnetic- andantiferromagnetic Kondo lattice model. I will show results for the metal-insulatortransition and magnetic ordering in the half-ﬁlled Kondo lattice and brieﬂy discuss
the relationship to orbital selective Mott states in multi-orbital models.

9

Abstracts: Poster Session on August 9th

P1

Spin-triplet superconductivity in the double-chain Hubbard
model with ferromagnetic exchange interaction
Tomonori Shirakawa (Department of Physics, Chiba University)
Mechanism of spin-triplet superconductivity has been one of the major issues in theﬁeld of strongly correlated electron systems. Here, the ferromagnetic interaction
between electrons is believed to play an essential role in the occurrence of triplet
superconductivity. In this paper, we study the simplest model in this context: i.e.,the model of two Hubbard chains coupled with Heisenberg-type ferromagnetic exchange interaction J. This model may be regarded as the degenerate two-band Hubbard model with the on-site Hund’s rule coupling in transition-metal oxides. Thismodel may also be regarded as the Hubbard chains with the interchain ferromagnetic interaction which may come from the ring-exchange mechanism in quasi-onedimensional organic materials [1].
We use the density-matrix renormalization group (DMRG) method and exactdiagonalization technique on small clusters to calculate the charge gap, spin gap,
binding energy, pair correlation functions, etc., as well as the anomalous Green’s
function of the model. We thereby show that the model contains the state of mobile‘rung-triplet’ pairs, i.e., spin-triplet superconductivity, in the wide parameter andﬁlling region. The binding energy, e.g., scales well with J when J is large. We also
show that the spin gap corresponding to th Haldane gap for the spin-1 Heisenberg
chain opens at half ﬁlling, the size of which becomes small away from half ﬁlling.
[1] Y. Ohta et al., Phys. Rev. B 72, 012503 (2005).

10

P2

Density matrix renormalization group study of dynamics in correlated electron systems with environment
Hiroaki Matsueda (Department of Physics, Tohoku University)
We study dynamical properties of one-dimensional correlated electrons coupled withenviroment. There are two topics in this study: one is whether the spin-charge separation is robust in materials where electrons strongly interact with phonons. Since
the separation provides novel optical properties such as gigantic third-order nonlinear response, it should be understood how the separation is realized in materials.
Starting with the Hubbard-Holstein model at half-ﬁlling, we calculate the singleparticle excitation spectrum by using the dynamical density matrix renormalizationgroup (DMRG) method. We ﬁnd that the spin-charge separation is robust in thepresence of the electron-phonon coupling. However, both of the spinon and holon
branches are affected by phonons. For interpretation of the DMRG results, we propose an effective model for the spectrum that is deﬁned by a superposition of spectra
for the Holstein model. The second topic is time evolution of correlated electrons
coupled with localized spins. One motivation is ultra-fast photoinduced phase transition recently observed in cuprates, manganites, and organic compounds. Here, theenergy dissipation plays a crucial role. Since the exchange energy is large in someoxides, the fast relaxation may be possible by emitting magnon excitations. Startingwith the extended double-exchange model, we study the transient spectrum of mobile electrons and time evolution of the spin-spin correlation for localized spins byusing the time-dependent DMRG method. We discuss the effect of the spin degrees
of freedom on the relaxation.

P3

Stability of One-dimensional Mott Insulators against Charge Fluctuations by the Density Matrix Renormalization Group Method
Isao Maruyama (Department of Applied Physics, University of Tokyo)
Collapse of one-dimensional Mott Insulators due to charge ﬂuctuation is studied
by the DMRG method, where the charge ﬂuctuation implies injection of electrons
and holes from out of the system. To introduce this “doping” effect, we construct
a Hamiltonian, which does not conserve a particle number but still preserves theparticle-hole symmetry. Due to the U(1) symmetry breaking term, zero temperatureﬂuctuation of the total particle number is ﬁnite even at half ﬁlling and is proportional
to the inverse of the Coulomb interaction in the strong coupling.
The U(1) symmetry breaking term in the present model can be regarded as a meanﬁeld of an inter-chain hopping when we use a string type decoupling. If the interchain hopping is irrelevant, total number of the 1D system is conserved and the 1D
Mott insulator is realized. Quantum phase transition collapsing the Mott gap is also
discussed.
We extend the DMRG method to treat a generic fermionic system with a U(1) symmetry breaking term where its total fermion number is not conserved.

11

P4

Numerical study of diluted orbital
Takayoshi Tanaka (Department of Physics, Tohoku University)
Various exotic phenomena in correlated electron systems are studied from the view
point of the internal degrees of freedom of electron, i.e. charge, spin and orbital
degrees of freedom in strong Coulomb interaction. Recently, dilution effects on theorbital ordered state are examined experimentally in KCuF3 which is a prototypicalmaterial showing the long range orbital order. It is revealed that, by replacing Cu
ion by Zn which does not have the orbital degree of freedom, a reduction of theorbital ordering temperature (T oo ) is more remarkable than that in diluted magnets,
and T oo disappears at a certain Zn concentration which is lower than the percolationthreshold. We investigate theoretically dilution effects in orbital systems.
(1) The classical eg orbital model is analyzed by the Monte-Carlo (MC) simulationand the cluster expansion method. We show T oo decreases more rapidly by increasing
dilution in comparison with the diluted magnets, and reproduce the experimental
results in KCu1−x Zn x F3 .
(2) We analyze the two dimensional version of the quantum eg orbital model, termed
the orbital compass model by quantum Monte-Carlo simulation. It is known that at
low temperatures, this model shows the orbital alignment along one direction in thetwo dimensional lattice, i.e. the directional order. We show that the directional ordering temperature decreases by dilution more rapidly than the diluted Ising model, butmore slowly than the classical compass model. This result implies that the quantum
effects stabilize the directional order.

P5

Eﬀects of Impurities in Quasi-One-Dimensional Haldane Antiferromagnets
Munehisa Matsumoto (ETH Zurich)
For spin-1 quasi-one-dimensional antiferromagnets that have quantum disorderedground states, the effects of magnetic and non-magnetic impurities are investigatedutilizing the quantum Monte Carlo method with the continuous-time loop algorithm.
Impurity-induced transition temperatures are determined with respect to the concentration of host spins and the nature of the phase transition between the paramagnetic
phase and the impurity-doped valence bond solid state is discussed. The qualitative
differences between the species of impurities in the impurity-induced phase transitions are discussed by investigating the local magnetic structure around impurities.

12

P6

Pairing Phase in Bosonic Systems with Correlated Hopping
Andreas Läuchli (IRRMA - EPF Lausanne)
Motivated by the physics of mobile triplets in frustrated quantum magnets, the properties of a two dimensional model of bosons with correlated-hopping are investigated. We study the phase diagram of this system as a function of density and thestrength of the correlated hopping term, based on Quantum Monte Carlo simulationsin the SSE formulation. We conﬁrm the existence of two different phases, ﬁrst reported in a mean-ﬁeld study: a conventional single particle bose condensed phase,and in addition a less studied phase where only pairs of bosons condense. We comment on the performance of the standard single worm SSE in the pairing phase, andon the possibility of using a “double worm” algorithm to improve the efﬁciency.
This work has been performed in collaboration with K.P. Schmidt and F. Mila (EPF
Lausanne).

P7

Bond-Dilution-Induced Quantum Phase Transitions in Heisenberg Antiferromagnets
Chitoshi Yasuda (Department of Physics and Mathematics, Aoyama Gakuin University)
Bond-dilution effects on a ground state of the S = 1/2 quantum antiferromagnetic(AF) Heisenberg model consisting of bond-alternating chains on a square lattice wasinvestigated by means of the quantum Monte Carlo simulations with the continuousimaginary-time loop algorithm. The magnitude of the stronger (weaker) intra-chaininteraction is put unity (α) and that of the inter-chain interaction J ′ . The groundstate of the pure system is the dimmer state with a ﬁnite spin gap for small α and J ′ .
When spins are randomly removed from the system in the dimer state (site dilution),a spin which formed a singlet pair with the removed spin before dilution becomes
nearly free, which we call effective spins. Between two of them, however, there
exists the ﬁnite interaction Jmn mediated by a sea of singlet pairs. Since the effective
interaction is AF (ferromagnetic) when the two effective spins are in the different(same) sublattices, an AF long-range order (LRO) is induced with an inﬁnitesimalconcentration of site dilution. When stronger bonds are randomly removed from thesystem in the dimer state (bond dilution), on the other hand, the effective spins arealways induced in pairs at both ends of the removed bonds. Since the two spins arelocated on the different sublattices, a singlet pair is reformed through the short-range
effective AF coupling Jaf of O(J ′2 ). In contrast to the site-diluted case, there exist
two effective interactions. For small concentration of dilution, if Jaf is sufﬁciently
larger than Jmn , the system is in the disordered phase. The phase transition between
the disordered and AF-LRO phases occurs when the magnitudes of Jaf and Jmn areequivalent.

13

P8

Low-energy properties of one-dimensional spin-orbital model
Hiroaki Onishi (Advanced Science Research Center, Japan Atomic Energy Agency)
By using a density-matrix renormalization group method, we investigate the groundstate properties and the spin-gap formation of a one-dimensional spin-orbital model,
in which the original SU(4) symmetry is broken due to the effect of the Hund’s rule
coupling.

P9

Surface and corner multifractality in two-dimensional symplectic
class
Hideaki Obuse (Condensed Matter Theory Laboratory, RIKEN)
We numerically calculated surface and corner multifractal exponents at the criticalpoint of the two-dimensional disordered system with the spin-orbital interaction. We
conﬁrm that the surface and the corner multifractal exponent satisfy a certain relation
derived from the conformal ﬁeld theory.

P10

Non-linear transport in a commensurate CDW and universal KPZ
ﬂuctuation
Takashi Oka (Department of Physics, University of Tokyo)
Solitonic excitations (kinks and anti-kinks) dominate the dynamics of a one dimensional commensurate CDW (e.g. polyacetylene) in ﬁnite electric ﬁelds. In ﬁnite
temperature, we predict that the dielectric breakdown of such systems shows featurescharacteristic of the KPZ universality class. We also propose (optical) experiments
to verify this phenomenon.

P11

Dynamical properties of photoexcited states in one-dimensional
dimerized Mott insulators
Nobuya Maeshima (Institute for Molecular Science)
Dynamical properties of photoexcited states are theoretically studied in a onedimensional Mott insulator dimerized by the spin-Peierls instability. Numericalcalculations combined with a perturbative analysis have revealed that the lowest
photoexcited state without nearest-neighbor interaction corresponds to an interdimer
charge transfer excitation that belongs to dispersive excitations. The adiabatic potential of this excited state as a function of the lattice dimerization has demonstrated
that the dimerized phase is destabilized by the photoexcitation from the ground state
to this excited state. We also discuss the purely electronic origin of midgap statesthat are observed in a latest photoexcitation experiment of an organic spin-Peierls
compound, K-TCNQ (potassium-tetracyanoquinodimethane).

14

P12

Quantum Monte Carlo study of the multiorbital Hubbard modelwith spin and orbital rotational symmetries.
Shiro Sakai (Department of Physics, University of Tokyo)
Combining the Trotter decomposition and a series expansion of the partition function
with respect to Hund’s exchange coupling, we develop a new quantum Monte Carlo(QMC) algorithm for multiorbital systems with spin and orbital rotational symmetries. While the conventional QMC method has difﬁculties to treat the spin-ﬂip andthe pair-hopping terms of the Hamiltonian, we show that our new approach enables
us to simulate these terms efﬁciently. To demonstrate this, we apply our algorithm
for studying ferromagnetism in the two-orbital Hubbard model within dynamicalmean ﬁeld theory (DMFT).
Our results reveal how important it is to account for the correct SU(2) symmetry ofHund’s exchange. Otherwise, i.e., for an Ising (Z2 ) symmetry, Curie temperatures
are grossly overestimated. We also calculate the t2g spectral functions of Sr2 RuO4
by three-band DMFT calculations with tight-binding parameters from the local density approximation as input and with proper rotational symmetries, which has been
impossible before.

P14

The Anderson transitions in 3D, 2D, and below 2D
Yoichi Asada (Department of Physics, Tokyo Institute of Technology)
We report our new precise estimates of the critical exponent for the divergence of thelocalization length at the Anderson transitions in 3D. We have ﬁnally conﬁrmed thatthe values of the critical exponent for three symmetry classes (orthogonal, unitary,and symplectic) are different. We have also estimated the scaling beta function for
the quasi-1D localization length, which indicates that the ﬁnite size scaling of thequasi-1D localization length depends on the symmetry in the metallic and criticalregions, but not in the strongly localized region.
We also report numerical study of the Anderson transition in systems with spinorbit coupling in 2D and below. Such systems are an exception to the predictionof Abrahams et. al. that there is no metallic phase in 2D and below. We haveestimated the critical exponent for the 2D Anderson transition in systems with spinorbit coupling, and then studied the quantum transport property in the 2D metallic
phase. Our results in the 2D metallic region support the Hikami-Larkin-Nagaoka’s
prediction that the 2D metals have perfect conductivity. We have also investigatedthe possibility of an Anderson transition below 2D. Our simulations on the Sierpinski
carpet suggest that an Anderson transition occurs even below 2D in the presence ofspin-orbit coupling. The lower critical dimension might be between 1D and 2D.

15

P15

Mean ﬁeld quantum annealing
Sei Suzuki (Department of Physics, Tokyo Institute of Technology)
Quantum mechanical approaches are attracted in computational sciences. The quantum annealing is a novel technique for optimization of various disordered problems.
It utilizes the dynamical motion of quantum state driven by handling quantum ﬂuctuations. As an important direction, we focus on realistic numerical methods to carryout the quantum annealing in classical computers. The mean ﬁeld quantum annealing, which we discuss, is a rough but non-trivial method. It is applicable to large
problem sizes and yields an answer fast. However it is not clear how the mean ﬁeld
method is valid. In our study we investigate the validity of this method for elementary models and clarify the property of this method in comparison with other known
optimization techniques. In my presentation, I will report our results of numericalcalculation and discuss the limitation of the mean ﬁeld quantum annealing. I will
also present an improvement of the mean ﬁeld approximation.

P16

New type of quantum liquid of spinless fermions on an anisotropic
triangular lattice
Chisa Hotta (Aoyama Gakuin University)
We propose a new type of liquid state of charges in the spinless fermion system ona triangular lattice under strong inter-site Coulomb interactions, V. In the strong
coupling limit (t = 0), the ground state is classical and disordered due to geometricalfrustration. The introduction of small t drives the system to a partially ordered phasewhich we call a ”pinball liquid”. A possibly long range ordered Wigner crystal solid
coexist with a liquid component which are moving around them like a pinball. Thisliquid is dominant over wide range of ﬁlling, even away from the regular triangle.
The phase diagram of the present system on an anisotropic triangular lattice is given
and a relevance to the organic crystal, θ-ET2 X is discsussed.

P17

Magnetization plateaux for distorted triangular antiferromagnet
Cs2 CuBr4
Shin Miyahara (Aoyama Gakuin University)
Cs2 CuBr4 is a new two-dimensional spin-1/2 system, where 1/3 and 2/3-plateauxhave been observed in external magnetic ﬁelds. It is expected that the magnetic
behaviors of the material can be well explained by a spin-1/2 two-dimensional antiferromagnetic Heisenberg model on a distorted triangular lattice. In the model,
there are two types of interactions, J1 and J2 , where J1 chains are coupled withinter chain interactions J2 . Using an exact diagonalization method, we investigate
magnetic properties in the plateau phases. In the 1/3-plateau phase, three-fold degenerate translational symmetry broken ground state is realized. On the other hand,
2/3-plateau has a translationally symmetry broken state where M = 1 and M = 1/3
chains along J1 bonds alternate with each other.
16

P18

Re-entrant quantum phase transitions with respect to the XXZ
anisotropy parameter in spin chains
Kiyomi Okamoto (Department of Physics, Tokyo Institute of Technology)
I will discuss the re-entrant quantum phase transitions in quantum spin chains when
the XXZ anisotropy parameter is run. In some cases, for example, we can see thesuccesive transitions such as TL-Neel-TL-Ferri, where TL means the TomonagaLuttinger spin-ﬂuid state. This phenomenon can be found in S = 1/2 spin chains
having three key words: XXZ anisotropy, trimer nature and frustration. We also
ﬁnd that four Berezinski-Kosterlitz-Thouless quantum phase transition lines meet
together at one point in the phase diagram on the plane of quantum parameters.

P19

Modiﬁcation of Directed-Loop Algorithm for Continuous Space
Simulation of Bosonic Systems
Yasuyuki Kato (Institute of Solid State Physics, University of Tokyo)
The directed-loop algorithm (DLA) is one of the most robust algorithms for quantum
Monte-Carlo simulation, and enjoys very broad applicability. Updates of world-line
conﬁgurations in DLA are done by a worm, which consists of a pair of discontinuity
points moving stochastically on world-lines and altering the state on the line justbehind itself. The direction of motion of a discontinuity point is altered only byscattering at vertices that are placed between world-lines or on a single world-linewith density determined by the Hamiltonian. However, when one applies the method
to a system such as the Bose-Hubbard model with t ≪ U (t is the hopping amplitudeand U is the on-site energy), the efﬁciency of the method is low because of highdensity of vertices due to large U. We improve DLA by omitting the vertices that
express the effect of U in this paper. The effect of U is reﬂected in other procedures.
We demonstrate the efﬁciency of the new method by applying it to the interacting
dilute Bose gas system in a discrete space that has the aforesaid difﬁculty.

17

Abstracts: Oral Session on August 10th

9:00-

ICAM session (I) — ICAMipedia
Daniel Cox (Institute for Complex Adaptive Matter of the University of California)
Prof. Daniel Cox, co-director of ICAM will lead a discussion on contributions to
the new ICAMipedia web pages where we can describe to the larger public (otherscientists, interested young people, educated public, and our community) the exciting
developments of our ﬁeld.

9:30-

Searching for a supersolid phase in three dimensions
Takafumi Suzuki (ISSP, University of Tokyo)
Since the fascinating features of solid helium were presented by torsional oscillator
experiments for the solid helium four [1], ordered states on the bosonic lattice models have received a great deal of attention. Recently, the existence of the supersolid
phase in the hard-core bosons on the triangular lattice was demonstrated by a numerical calculation [2]. Such bosonic lattices can be experimentally realized by trapping
the ultra-cold bosonic atoms into the optical lattices. It is useful to study the orderedstates on the bosonic lattice models in order to clarify the characteristics of the supersolid state. In this study, we investigate the ordered states of the hard-core bosons
with unfrustrated hopping and nearest-neighbor repulsion on the face-centered cubic(FCC) lattice. The static structure factors and the superﬂuid density are calculated,using a quantum Monte Carlo method. At the half ﬁlling and the three-quarter ﬁlling,
the ordered phases with the crystalline lattice appear below the critical temperature.
However, between the two ﬁllings, there appears the phase in which the long-range
diagonal order and the superﬂuidity coexist. This phase is in contrast to the orderedphases observed for Ising spins [3]. We discuss more details of the supersolid stateson the FCC lattice.
[1] E. Kim and M. H. W. Chan, Nature 427, 225 (2004); Science 305, 1941 (2004).
[2] S. Wessel and M. Troyer, Phys. Rev. Lett 95, 127205 (2005).
[3] K. Binder, et. al., Acta metall. 29, 1655 (1981).

18

10:00-A new high ﬁeld phase in the frustrated 2D dimer spin system
SrCu2 (BO3 )2Masashi Takigawa (ISSP, University of Tokyo)
The frustrated 2D dimer spin system SrCu2 (BO3 )2 shows magnetization plateaus at
1/8, 1/4 and 1/3 of the saturated magnetization, where symmetry breaking superlattices of triplets were observed by NMR experiments (Science 298 (2002) 395). How
the spin density distribution evolves between the plateaus is a highly non-trivial issue. One possibility is that the hopping of triplets melts the superlattice and theBose-condensed phase with the transverse AF order appears instead. Another possibility is the ”supersolid” phase, in which a superlattice of the longitudinal component
coexists with the transverse AF order. The nature of the phase may be even more
complicated by the presence of Dzyaloshinskii-Moriya interaction, which produces
an effective staggered ﬁeld (J. Phys.:Condens Matter. 17 (2005) L61). We performed
11
B NMR experiments in the ﬁeld up to 31 T above the 1/8-plateau phase. The NMR
spectra show discontinuous change upon leaving the 1/8-plateau. However, the maximum hyperﬁne ﬁled at the B nuclei remains nearly unchanged, indicating that thesuperlattice of largely polarized triplet dimers still persists above the 1/8 plateau
phase. The ordering temperature in the high ﬁeld phase agrees with the peak of thespeciﬁc heat reported by Tsujii et al. (cond-mat/0301509). The sharp ﬁne structuresof the NMR spectra in the plateau phase, however, become broadened as the ﬁeld
increases. Possible scenarios to explain the evolution of NMR spectra will be discussed. This work was done in collaboration with S. Matsubara1, M. Horvatic, C.
Berthier, H. Kageyama and Y. Ueda.

19

11:00-Magnetic Quantum Phase Transitions and Critical Behavior in
TlCuCl3 and KCuCl3
Hidekazu Tanaka (Tokyo Institute of Technoloby)
TlCuCl3 and KCuCl3 are magnetically characterized as three-dimensionally coupled
spin-dimer system. Their ground states are spin singlets with excitation gaps ∆/kBof 7.5 K and 31 K, respectively. The origin of the gap is the strong antiferromagnetic
exchange interaction in the chemical dimer to form a spin dimer. In a magnetic ﬁeld,
which is higher than the critical ﬁeld Hc corresponding to the gap, these systems canundergoes magnetic ordering with the transverse-ordered moments [1,2]. The ﬁeldinduced magnetic quantum phase transition (QPT) in TlCuCl3 has been extensively
studied by various techniques. The results obtained were in accordance with theory
which describes the ﬁeld-induced magnetic QPT as the Bose-Einstein condensationof spin triplets [3]. For example, the critical exponent φ of the phase boundary
deﬁned by T (H) ∝ (H − Hc )1/φ is close to φBEC = 3/2 derived from the magnon BEC
theory [3,4]. Under a hydrostatic pressure P, the gap decreases and closes completely
at Pc = 0.42 kbar and 8.2 kbar for TlCuCl3 and KCuCl3 , respectively [5]. For
P > Pc , these systems undergoes antiferromagnetic ordering, which is characterized
by the same ordering vector as that for the ﬁeld-induced magnetic ordering. The
gap and Néel temperature are presented as functions of pressure. The occurrence of
this pressure-induced magnetic QPT is attributed to the decrease of the intradimer
interaction and the increase of interdimer interaction with applied pressure. The
present results are discussed in connection with recent theory [6,7].
[1] H. Tanaka et al.: J. Phys. Soc. Jpn. 70 (2001) 939.
[2] A. Oosawa et al.: Phys. Rev. B 66 (2002) 104405.
[3] T. Nikuni et al.: Phys. Rev. Lett. 84 (2000) 5868.
[4] N. Kawashima: J. Phys. Soc. Jpn. 73 (2004) 3219.
[5] K. Goto et al.: J. Phys. Soc. Jpn. 73 (2004) 3254, cond-mat/0602540.
[6] M. Matsumoto et al.: Phys. Rev. B 69 (2004) 054423.
[7] O. Nohadani et al.: Phys. Rev. B 72 (2005) 024440.

20

11:30-A Bose-Einstein condensate of magnons in anisotropic quantum
magnets BaCuSi2 O6 and NiCl2−4 SC(NH2 )2Marcelo Jaime (National High Magnetic Field Laboratory, Los Alamos National Lab.)
Quantum magnets BaCuSi2 O6 [1] and NiCl2−4 SC(NH2 )2 [2] attracted signiﬁcantattention in the last years, because magnetic ﬁelds can be used to tune a canted
antiferromagnetic state regarded as a Bose-Einstein condensate of magnons. The
coupling between spin and lattice degrees of freedom, however, was not yet studied in the ordered state. Different anisotropy in their crystallographic lattices andtheir spin arrangements, spin S = 1/2 Cu2+ dimers in BaCuSi2 O6 and S = 1 Ni2+
in NiCl2−4 SC(NH2 )2 , are responsible for different degree of spin-lattice coupling.
While the former only displays weak lattice effects, the later shows a signiﬁcantmagnetostriction that changes sign as the canting angle between spins is reduced
and the spin arrangement evolves gradually from AFM at the critical ﬁeld Hc1 , to
FM at the saturation ﬁeld Hc2 . Recent speciﬁc heat, magnetocaloric effect and magnetostriction measurements at high magnetic ﬁelds will be discussed for these two
fascinating compounds.

12:00-

Geometrical Frustration and Dimensional Reduction at a Quantum Critical Point
Cristian Batista (Condensed Matter and Statistical Physics, Los Alamos National Lab.)
Competition between ground states near a quantum critical point is expected tolead to unconventional behavior in low dimensional systems. New phases of matter have been predicted, and explanations proposed for unsolved problems including non-Fermi liquid behavior and high temperature superconductivity using twodimensional (2d) theories. In this talk, I will present a theory that describes theBose-Einstein condensate (BEC) quantum critical point (QCP) in layered systems
with a frustrated inter-layer coupling. I will demonstrate that the main effect of thisgeometric frustration is to reduce the dimensionality of the QCP (its critical exponents are the ones expected for a 2d system). In addition, I will compare this theory
with the ﬁrst experimental evidence of dimensional reduction at a QCP observed in
the Mott insulator BaCuSi2 O6 (Han Purple).

21

14:00-ICAM session (II) — I2CAM Fellowships
Daniel Cox (Institute for Complex Adaptive Matter of the University of California)
Prof. Daniel Cox will lead a session in which participating junior scientists develop
ideas for exchange fellowships through ICAM based upon the science of this meeting.

14:30-

Field-Induced Quantum Critical Phenomena in Quasi-1D Spin
Systems
Toru Sakai (Japan Atomic Energy Agency/Spring-8)
Using the numerical diagonalization based on the Lanczos algorithm, we investigate the magnetization process of several spin ladder systems with the next-nearestneighbor interaction, or the ring exchange interaction. The ﬁnite size scaling analysis
based on the conformal ﬁeld theory and the recently developped level spectroscopy
method reveal that a magnetization plateau would appear at half the saturation magnetization, if the next-nearest-neighbor or ring exchange interaction is sufﬁciently
large. In addition the mean-ﬁeld approximation for the interladder interaction suggests that the quasi-1D system possibly exihibit a ﬁeld-induced incommensurate order in some regions close to the magnetization plateau. Several phase diagrams in
the ground state of the 1D system are also presented.

15:00-

Emergence of Long Period Antiferromagnetic and Ferrimagnetic
Orders Due to Anisotropy Modulation in High Spin Heisenberg
ChainsKazuo Hida (Department of Physics, Saitama University)
In integer spin antiferromagnetic Heisenberg chains, the easy plane single-site
anisotropy D(> 0) destroys the Haldane ground state leading to the large-D phase
while the easy axis single-site anisotropy (D < 0) drives the Haldane state into the
Neel ordered state. In this context, it is an interesting issue to investigate how theground states of the quantum spin chains are modiﬁed if the easy-axis and easyplane D-terms coexist in a single chain. In the present study, we investigate theground states of the high spin Heisenberg chains with period 2 modulation of single site anisotropy. It turns out that various phases such as Haldane phase, large-D
phase, Tomonaga-Luttinger liquid phase, Neel phases of various structures and ferrimagnetic phase appear depending on the strength of modulation and spin magnitude.

22

16:00-

Tomonaga-Luttinger liquid induced by a magnetic ﬁeld in a
gapped quasi-1D antiferromagnet
Masayuki Hagiwara (High Magnetic Field Laboratory, Osaka University)
The Tomonaga-Luttinger liquid (TTL) is a universal low-temperature state of gapless, one-dimensional (1D) quantum systems. 1D antiferromagnets having an energy gap are expected to become a TLL, when a strong magnetic ﬁeld is applied
to collapse the energy gap. To date, however, all experimental evidence in theseantiferromagnets has been either controversial or circumstantial. In the spin-1 bondalternating antiferromagnet NTENP, we have observed an unambiguous signature of
a TLL: a linear temperature (T) dependence of the magnetic speciﬁc heat (Cmag ). The
linear Cmag appears only in magnetic ﬁelds above the critical value Hc = 9.3T and theSommerfeld constant Cmag /T increases as the ﬁeld is reduced toward Hc . This ﬁeld
dependence agrees well with the results of our calculation, providing a conclusive
evidence for a TLL.

16:30-

Quantum Critical ”Opalescence”
Masatoshi Imada (Department of Applied Physics, University of Tokyo)
Divergent carrier-density ﬂuctuations equivalent to the critical opalescence of gasliquid transition emerge around a metal-insulator critical point at a ﬁnite temperature.
In contrast to the gas-liquid transitions, however, the critical temperatures can belowered to zero, which offers a challenging quantum phase transition. We present
a microscopic description of such quantum critical phenomena in two dimensions.
The conventional scheme of phase transitions by Ginzburg, Landau and Wilson isviolated and an unconventional universality appears. It offers a clear insight into
the criticalities of metal-insulator transitions associated with Mott or charge-ordertransitions. Fermi degeneracy involving the diverging density ﬂuctuations generates
emergent phenomena near the endpoint of the ﬁrst-order transition and must shed
new light on remarkable phenomena found in correlated metals like unconventional
cuprate superconductors.

23

17:00-Phase-space methods for fermions: bounded distributions andstochastic gauses
Joel Corney (Department of Physics, The University of Queensland)
Gaussian Quantum Monte Carlo Methods are a class of simulation methods based onphase-space representations of quantum states. Successful simulations of the Hubbard model showed that, for this case, GQMC did not suffer the same sort of ‘classic’sign problem as other comparable methods. However, GQMC does have its own difﬁculties. A known issue in phase-space methods is to do with the boundedness of
the underlying distribution, and the ability of stochastic equations to sample this distribution. I will cover recent investigations into the type of distributions that arise forinteracting systems, the effectiveness of ‘stochastic gauges’ to control distribution
tails, and efﬁcient simulation methods.

17:30-

Highly Correlated Electrons on Triangular Lattice; Mott Criticality, Spin Liquid and Superconductivity
Kazushi Kanoda (Department of Applied Physics, University of Tokyo)
The layered organics, κ-(ET)2 X, are model systems for the study of strongly correlated half-ﬁlled-band electrons. Here we present two progresses in the Mott physics
through the transport and NMR studies on this family of materials.
One is the Mott criticality in 2D. κ-(ET)2 Cu[N(CN)2 ]Cl is a Mott insulator with aquite low critical pressure to Mott transition. The resistance measurements of thismaterial under precisely controlled pressure showed that the ﬁrst-order Mott transition has a critical endpoint at 40 K, where the resistive jump vanishes and criticalpressure derivative of resistance is divergent. Remarkably, the transport critical exponents obtained do not belong to any universality class known so far. The implication of this ﬁnding is discussed. A recent NMR study on the Mott criticality is alsopresented.
The other is the realization of the spin liquid and its Mott transition. The Mott
insulator κ-(ET)2 Cu2 (CN)3 has a nearly isotropic triangular lattice and is a model
system of frustrated quantum spins. The 1 H and 13 C NMR experiments showed no
indication of magnetic ordering down to 30 mK. The spins are likely in the quantum
liquid state. Under pressure, it undergoes Mott transition to the Fermi liquid whichshows superconductivity at low temperatures. We present the pressure-temperaturephase diagram and the NMR/transport results on the nature of the spin liquid andsuperconductivity.
This work is a collaboration with F. Kagawa, Y. Shimizu, Y. Kurosaki, H. Kasahara,
T. Kobashi, K. Miyagawa, M. Maesato and G. Saito.

24

Abstracts: Oral Session on August 11th

9:00-

Finite Temperature Eﬀects on the Excitation Spectrum in Quantum Critical Magnetic Insulators
Christian Rüegg (Department of Physics and Astronomy, University College London)
The compound TlCuCl3 represents a model system of dimerized quantum spinswith strong interdimer interactions. We have investigated the triplet dispersion as
a function of temperature by inelastic neutron scattering experiments in zero magnetic ﬁeld. The description of Troyer, Tsunetsugu, and Würtz provides an appropriate quantum statistical model for dimer spin systems at ﬁnite temperature, where
many-body correlations become particularly important [Ch. Rüegg et al., Phys. Rev.
Lett. 95, 267201 (2005)]. The temperature-dependence of the excitation spectrum issubsequently investigated by the same experimental technique at ﬁnite ﬁeld aroundthe quantum critical point at Hc , where the triplet gap is closed at T = 0 K andﬁeld-induced BEC of magnons occurs. The observed renormalization effects in thequantum critical region as well as the phase with long-range magnetic order will be
discussed and compare to the zero-ﬁeld results.

25

9:30-Ion Exchange as a Tool to Explore Two-Dimensional Square Lattice Antiferromagnets
Hiroshi Kageyama (Dept. of Chemistry, Graduate School of Science, Kyoto Univ.)
Soft chemical approach provides us new routes for the construction of new magnetic materials. Two-dimensional (2D) S = 1/2 square-lattice antiferromagnets(CuX)LaB2 AO7 (X=Cl, Br; B=Nb, Ta) have been obtained by the ion exchange
between Dion-Jacobson layered perovskites RbLaB2 O7 and CuX2 . Here the magnetic [CuX]+ layer is well separated by nonmagnetic perovskite slabs so that 2D
magnetic properties are expected. The obtained materials shows a variety of magnetic behaviors. (CuCl)LaNb2 O7 has a spin singlet ground state with an energy gapof 2.3 meV to the ﬁrst excited triplet state [1]. Application of the magnetic ﬁeld
leads to the magnetic order described by the BEC of magnons [2]. On the other
hand, (CuBr)LaNb2 O7 undergoes a magnetic ordering of the stripe tope at 31 K
and the analysis of the data indicates strong frustration in the layer. It is found that
(CuCl)LaTa2 O7 also exhibits a long-range magnetic ordering at 6 K. We have recently succeeded to obtain the solid solution series (CuCl x Br1−x )Nb2 O7 (0 < x < 1)
and (CuCl)La(Nb1−y Tay )O7 (0 < y < 1), which allows to investigate the magnetic
phase diagrams between the spin-liquid state and the antiferromagnetic state. The
structural and magnetic properties of these systems will be presented.
[1] H. Kageyama et al., J. Phys. Soc. Jpn. 74 (2005) 1702.
[2] H. Kageyama et al., J. Phys. Soc. Jpn. 74 (2005) 3155.

10:00-

Magnetic multipole orders in frustrated ferromagnets
Tsutomu Momoi (RIKEN)
We present a new scenario for the breakdown of ferromagnetic order in twodimensional quantum magnets with competing ferromagnetic and antiferromagnetic
interactions. Dynamical effects lead to the formation of magnon bound states, which
undergo Bose-Einstein condensation, giving rise to magnetic multipole order. This
scenario is explored in some detail for extended Heisenberg models on a square lattice and a triangular lattice. On a square lattice, two-magnon bound states are moststable, giving rise to bond-centered spin nematic (quadratic) order. In particular, we
present numerical evidence conﬁrming the existence of a state with d-wave nematic
correlations but no long range spin order, lying between the saturated ferromagnetic
and antiferromagnetic phases. On the other hand, in a multiple spin exchange model
on a triangular lattice, three-magnon bound states are most stably formed, leading to
the appearance of magnetic octupole order.

26

11:00-

Duality and ﬁnite-size scaling analysis of the two-dimensional diluted Villain model
Yutaka Okabe (Department of Physics, Tokyo Metropolitan University)
The effect of dilution on the phase transition has been extensively studied since thepioneering work by Harris. However, not so much attention has been given to thedilution effect on the Kosterlitz-Thouless (KT) transition. The duality plays an important role in the phase transition. We here investigate the two-dimensional diluted
Villain model, which has the exact duality mapping, by using the Monte Carlo simulation with the cluster algorithm. We examine the duality relation which is expected
to hold for the two KT transition points of the diluted Villain model. We propose anduse an ab-inito ﬁnite-size scaling analysis for the KT transition.

11:30-

Kondo Problems in Quantum Critical Environments
Hideaki Maebashi (ISSP, University of Tokyo)
The asymptotic low temperature singularities in the thermodynamic and transport
properties of many solids appear to be due to impurities. While several impurity
models have quantum critical points (QCP’s), where such singularities may be expected, they require special symmetries unlikely to be present in real systems. An
alternate possibility is that the environment around the impurities is near a QCP,
so that singular low energy ﬂuctuations are present. We investigate the problem
which couples such ﬂuctuations of the quantum critical environment to the quantum
ﬂuctuation or Kondo effect of ordinary spin-1/2 magnetic impurities (not requiring
any special symmetries) [1,2]. We show that the problem maps onto a multichannel problem. A variety of ﬁxed points is discovered asymptotically near the QCP.
Among these is a new variety of stable ﬁxed point of a multichannel Kondo problem which does not require any channel symmetries. At this point Kondo screening
disappears but coupling to the critical spin ﬂuctuations remains. Besides its intrinsic
interest, the problem is an essential ingredient in the problem of antiferromagnetic
QCP’s in heavy fermions.
[1] H. Maebashi, K. Miyake, and C.M. Varma, Phys. Rev. Lett. 88 (2002) 226403.
[2] H. Maebashi, K. Miyake, and C.M. Varma, Phys. Rev. Lett. 95 (2005) 207207.

27

12:00-Magnetic structure in inhomogeneous systems and timedependent systems
Seiji Miyashita (Department of Physics, University of Tokyo)
We will discuss ordering structure in inhomogeneous systems and time-dependent
systems. The former is motivated by the problem to ﬁnd in what condition the
super-solid state appears. So far, the condition has been studied in uniform system. However, by the recent development of nanoscale design of material and alsoof the technique of optical lattice, we may control inhomogeneous structure of thelattice. Here we will study a system where the system parameters change in spaceand study the local ordering patterns. In particular, we explore the possibility to ﬁnd
the coexistence of the spatial density order (DLRO) and the super-ﬂuidity (ODLRO).
We study the following spin model (Matsubara-Matsuda model). The latter is motivated by the experiment on the optical lattice where the system is changed from asolid state due to the periodic optical potential to a super-ﬂuid state (BEC). We will
discuss the metastable or spinodal phenomena in pure quantum mechanical systems.

14:00-

A numerical algorithm for the eigenvalue distribution of nonHermitian matrices
Naomichi Hatano (Institute of Industrial Science, University of Tokyo)
We have developed a numerical algorithm of computing the eigenvalue distributionof non-Hermitian matrices with the memory size of O(N), where N is the dimension of the matrix. The algorithm basically computes the norm of the Green’s function from its largest singular value, which involves (i) the matrix inversion of nonHermitian matrices by the biconjugate gradient method and (ii) the calculation of thelargest eigenvalue of a Hermitized matrix by the Lanczos method.

28

14:30-The correlation density matrix: new tool for analyzing exact diagonalizations?
C. L. Henley (Institute of Industrial Science, University of Tokyo)
Is there an unbiased way to determine numerically any important correlations, even
unforeseen ones, in a lattice model of strongly interacting spins or fermions? Let
ρ̂A , ρ̂B , and ρ̂A∪B be the reduced, many-body density matrices for (respectively) the
small clusters A and B, offset by a vector r, and their (disconnected) union. Then all
possible correlations are contained in the “correlation density matrix”, ρ̂C (r) ≡ ρ̂AB −∑ρ̂A ⊗ ρ̂B . Via singular-value decomposition we write ρ̂corr = i λi Φ̂i (A)Φ̂′i (B), whereΦ̂i and Φ̂′i are normalized operators on the respective clusters; the terms represent
different correlation functions, their strength given by the magnitudes |λi |.
The procedure, tested on a ladder model of spinless fermions, correctly identiﬁed
the growth of superconducting correlations, but only a DMRG-based version of themethod would have a chance to probe the (Luttinger liquid) criticality. We proposethat the correlation density matrix is more promising for non-critical states: to detect
any strong order in an ordered state, or to conﬁrm the nonexistence of any order in aspin liquid state.

15:00-

Ferromagnetism and Quantum Statistics
Masaki Oshikawa (ISSP, University of Tokyo)
Although ferromagnetism has been known to mankind for a long time, its mechanism
is rather nontrivial. Ferromagnetism occurs because the electron spins are alignedin the same direction spontaneously, but there is no such explicit fundamental interaction. Rather, it must be caused primarily by quantum effect and spin-independent
Coulomb interaction. However, Fermi statistics of electrons is an obstacle to realize
ferromagnetism. In fact, Eisenberg and Lieb proved that a wide range of “spin-1/2
boson” models with repulsive interaction has a completely spin-polarized groundstate.
In this talk, I discuss a possible mechanism of ferromagnetism in spin-1/2 fermions.
We consider a U = ∞ Hubbard model with a magnetic ﬂux, which only couples
to the orbital motion and not to the spin. When the ﬂux per plaquette matches thedensity of fermions, the fermion may be transmutated into boson and the ferromagnetism could be realized. We study the model numerically and ﬁnd an evidence thatthe ferromagnetism is indeed realized by the statistical transmutation.
[1] Y. Saiga and M. O., Phys. Rev. Lett. 96, 036406 (2006).

29

15:30-Flowgram method for precise studies of poly-critical points anddeconﬁned criticality as a theory of weak ﬁrst order transitions
Nikolay Prokof’ev (Department of Physics, University of Massachusetts, Amherst)
We performed a comparative Monte Carlo study of the easy-plane deconﬁned critical point (DCP) action and its short-range counterpart to reveal close similarities
between the two models for intermediate and strong coupling regimes. For weakcoupling, the structure of the phase diagram depends on the interaction range: while
the short-range model features a tricritical point and a continuous U(1)×U(1) transition, the long-range DCP action is characterized by the runaway renormalization
ﬂow of coupling into a ﬁrst (I) order phase transition. We develop a “numericalﬂowgram” method for high precision studies of the runaway effect, weak I-ordertransitions, and poly-critical points. We prove that the easy-plane DCP action is theﬁeld theory of a weak I-order phase transition between the valence bond solid andthe easy-plane antiferromagnet (or superﬂuid, in particle language) for any valueof the weak coupling strength. Our analysis also solves the long standing problemof what is the ultimate fate of the runaway ﬂow to strong coupling in the theoryof scalar electrodynamics in three dimensions with U(1)×U(1) symmetry of quartic
interactions.

16:00-

Deconﬁned quantum criticality in a 2D Heisenberg model with
four-spin interactions
Anders Sandvik (Department of Physics, Boston University)
I will discuss the valence-bond-solid (VBS) phase and the Neel-VBS quantum phasetransition in a 2D S = 1/2 Heisenberg model which in addition to the standard
nearest-neighbor exchange includes a four-spin interaction (a subset of the foursspin cyclic exchange terms). Quantum Monte Carlo simulations, carried out in thevalence bond basis, show evidence for deconﬁned quantum criticality in this model.
As predicted theoretically, the spin correlation exponent η is anomalously large andthere are explicit signs of an emergent U(1) symmetry at the critical point.

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