令 和 ５ 年 度
京 都 大 学 大 学 院 理 学 研 究 科

Ｄ Ｃ ３ 回 生 研 究 発 表 会
要旨集

２０２３年１１月２４日（金）物 理 学 第 一 分 野

物理学第一分野ＤＣ３回生研究発表会
場所：理学研究科５号館 ５階・第４講義室（５２５号室）+Zoom
発表：２０分（別に質問１０分程度）
２０２３年１１月２４日（金）９：００～

目

開始

次

１．Nonlinear optical response in strongly correlated electron systems
Akira Kofuji（ ９：００）・・・・・ １
２．Terahertz Doppler-free spectroscopy in rotational levels of gas-phase molecules
Kohei Eguchi（ ９：３０）・・・・・ ２
３．Wavenumber of Self-organized Stripes in Liquid Crystal Gels
Akinori OOKA（１０：００）
・・・・・ ３
１０：３０～１０：４０ 休憩
４．Theoretical Study of Invertible States Using Matrix Product States
Shuhei Ohyama（１０：４０）
・・・・・ ４
５．Luminescence fine structure and exciton–phonon interactions
in single halide perovskite nanocrystals
Kenichi Cho（１１：１０）・・・・・ ５
６．Impact of intraband transitions in high-order harmonic generation from solids
Kotaro Nakagawa（１１：４０）・・・・・ ６
１２：１０～１３：１０ 昼休み
７．Bulk-boundary correspondence in non-Hermitian point-gap topological phases
Daichi Nakamura（１３：１０）・・・・・ ７
８．Topology and Strong correlation effect of Hidden symmetry breaking superconductor
Kosuke Nogaki（１３：４０）
・・・・・ ８
９．Quantum algorithm for persistent Betti numbers and topological data analysis
Ryu Hayakawa（１４：１０）
・・・・・ ９

１４：４０～１４：５０ 休憩
１０．Stability of Symmetry-Protected Topological Phases
as Resources of Measurement-Based Quantum Computation
Riku Masui（１４：５０）
・・・・・１０
１１．Dynamic coupling of dynamics of bilayer s and Brownian motion of colloidal particles
Shingo YOSHIOKA（１５：２０）
・・・・・１１

Nonlinear optical response in strongly correlated electron systems
Condensed Matter Theory Group

Akira Kofuji

Abstract We have studied the gap dependence of high-order harmonic generation in two-level systems
and found an unconventional gap dependence in the strongly light-matter coupled regime. Also, we haveinvestigated two-particle correlation effects on nonlinear optical phenomena and revealed that
two-particle fluctuations beyond the mean-field level significantly enhance the photocurrent.
© 2023 Department of Physics, Kyoto University

Nonlinear responses have been widely studied because of their great potential to reveal states inmaterials, such as ferroelectric domains[1], Berry curvature dipole in topological materials[2], andso on. Recently, nonlinear responses in strongly correlated electron systems have also attracted
much attention, and various experiments have been conducted[3,4,5]. For example, in a Mott
insulator Ca2RuO4, an unconventional gap dependence of High harmonic generation(HHG) has
been observed[3], which cannot be understood by the conventional three-step model. Also, in 1d
ferroelectric organics (TMTTF)2X(X=AsF6 and PF6), a photoinduced increase of short-range
correlations has been observed[4], and, in a chiral magnet MnSi, nonlinear nonreciprocal transport
is enhanced above the transition temperature[5]. All these experiments imply a close relationshipbetween interactions and nonlinear responses. However, most theoretical studies on nonlinear
responses rely on independent particle approximation[6], and to what extent interactions andfluctuations affect nonlinear responses are not fully understood.
In this presentation, first, we discuss the gap dependence of High harmonic generation in
two-level systems without interactions[7]. The simplicity of a two-level system makes it possible toinvestigate its gap dependence in broad parameter regions varying the light-matter coupling and therate of relaxation. As a result, we find that when the Rabi frequency is sufficiently large comparedto the gap width, the HHG intensity grows as the gap width is increased, and the enhancement rateobeys a scaling law, which is independent of the incidental frequency. Also, we find that relaxation
processes are not essential but increase the visibility of the gap dependence.
Next, we discuss the dynamics of two-particle correlations and their connection with nonlinear
responses in the 1D interacting Rice-Mele model[8]. We utilize the correlation expansion method
by Fricke[9] and calculate the nonlinear conductivity and the time evolution of two-particle
correlations in a unified framework. As a result, we find that two-particle fluctuations can markedly
enhance the nonlinear photovoltaic effect and, on the other hand, suppress the linear opticalconductivity slightly. Furthermore, in the photoinduced steady state, the short-range two-particle
fluctuation increases compared to that in the equilibrium. We will discuss how the interaction isrelated to these results by transforming the interaction to the band basis and consideringcorresponding two-particle correlations.
References[1] Y. Zhang et al., npj Comput. Mater. 4, 39 (2018).
[2] I. Sodemann and L. Fu, Phys. Rev. Lett. 115 216806 (2015).
[3] K. Uchida et al., Phys. Rev. Lett. 128, 127401 (2022).
[4] H. Itoh et al., Phys. Rev. Res. 3, L032043 (2021).
[5] T. Yokouchi et al., Nat. Commun. 8, 866 (2017).
[6] J. E. Sipe and A. I. Shkrebtii, Phys. Rev. B 61, 5337 (2000).
[7] A. Kofuji and R. Peters, Phys. Rev. A 108, 023521 (2023)[8] In preparation.
[9] J. Fricke, Ann. Phys. 252, 479 (1996).

Terahertz Doppler-free spectroscopy in rotational levels of
gas-phase molecules
Solid State Spectroscopy Group

Kohei Eguchi

Abstract We applied Doppler-free spectroscopy to rotational transitions of acetonitrile in the terahertz
region. Pressure dependence of the homogeneous width was confirmed beyond the Doppler-limit. The
homogeneous width in the zero-pressure limit was 32 kHz and should be originated from transit-time
broadening (~36 kHz) and lifetime broadening.
© 2023 Department of Physics, Kyoto University

Rotational transition of gas-phase molecules appears in the terahertz (THz) frequency region. It
is specific to the molecules, so called fingerprint spectrum and widely used for material analysis andfor frequency calibration in fields ranging from chemistry and biotechnology to astrophysics:
Numerous lines are listed in databases such as NASA JPL [1] and HITRAN [2]. On the other hand,due to the lack of high-power, narrow-linewidth terahertz light sources, high-precision spectroscopy
methods developed in the electronic transition region have rarely been applied to rotationaltransitions [3, 4], and their early realization has been awaited.
In this study, we realized THz Doppler-free spectroscopy, a nonlinear spectroscopy method thatobserves a homogeneous width narrower than the Doppler-width, using an ultranarrow-linewidth
THz source less than 1 Hz, and applied it to rotational transitions of gas-phase acetonitrile molecules.
Since the available THz power is less than 10 μW, acetonitrile molecules with large oscillator
strength of rotational transitions were used to realize the saturation region.
Figure 1 shows Doppler-free spectra for several sample pressures measured at room temperature.
A narrow dip structure was observed at the center of the Doppler-broadened (~600 kHz) peak. The
pump laser power was 6 W which was 120 times less than the power in the previous study [3]. We
determined pressure dependence of homogeneous width () as shown in Fig. 2. The linear
dependence suggests the collisional broadening. We found that the homogeneous width in the zeropressure limit is 32 kHz and should be originated from the transit-time-broadening (~36 kHz) andlifetime broadening [5].
0.3 Pa
0.2 Pa
0.1 PaFig. 1: Pressure dependence of the absorption spectrumof (J, K) = (15, 0) → (16, 0) rotational transition in
acetonitrile under THz pumping in several pressures.
dots: measured data, lines: fitting curves.

Fig. 2: Pressure dependence of homogeneous width.
Closed circles: homogeneous width obtained by thefitting (shown in Fig. 1). dashed line: linear fitting
curve.

References[1] H. M. Pickett et al., J. Quant. Spectrosc. Radiat. Transf. 60, 883–890 (1998).
[2] L. S. Rothman et al., J. Quant. Spectrosc. Radiat. Transf. 60, 665–710 (1998).
[3] M. Wienold et al., Opt. Express 26,6692-6699 (2018).
[4] R. Voigt et al., Opt. Express 31,13888-13894 (2023).
[5] W. Demtröder, Laser spectroscopy, vol. 2 (Springer, 2008).

Wavenumber of Self-organized Stripes
in Liquid Crystal Gels
Soft Matter Physics Laboratory

Akinori OOKA

Abstract In liquid crystal gels, self-organized stripe domains appear in response to external stimuli. To
determine what governs stripe width, anisotropy in polymer steps and surface anchoring strength werevaried, leading to significantly altered stripe widths. A comparison with theory suggests that liquid crystal
elasticity is more dominant than previously believed.
© 2023 Department of Physics, Kyoto University

Liquid crystal nematic gel (LCG) has a structure in which a
polymer network is swollen with liquid crystal molecules.
The polymer chain and the liquid crystal interact, leading topolymer chain rearrangement when the director changes [1].
It is known that both the elasticity of the polymer networkand the Frank elasticity of the liquid crystal govern thephysical properties of the gel. The former becomes dominant
when the liquid crystal director is heterogeneous; theopposite is true for the latter. Due to this competition,
self-organized stripe domains appear in LCG under certain
external stimuli due to non-uniform rotation of the director
Fig.1：Change in free energy due to polymer[1]. The free energy and wavenumbers of such a striped LCG
anisotropy r
have been calculated based on this picture [2], but theirquantitative accuracy compared to experiment remains unexplored.
The purpose of this study is to experimentally determine the contribution of polymer chain and liquid crystal
elasticity to stripe formation. Specifically, I prepared and observed LCGs and investigated how variations inpolymer chain anisotropy and surface anchoring strength lead to changes in stripe wavenumber.
Firstly, LCGs were produced with different polymer chain anisotropy. LCGs polymerized at lower temperatures
lead to polymer networks with more anisotropy in polymer segment step direction [1]. Anisotropy r of the chain is
1 when the polymer chain is isotropic and increases with increasing anisotropy in the direction of the initial
director. In theory, increasing the anisotropy r of the chain alone should increase the wavenumber of the stripes(Fig.1). The opposite was true in experiments. One possible cause of this is that the polymer chains become
stretched and hardened, making it difficult for the liquid crystal molecules to rotate.
This leads me to believe that the ease of rotation of the director has a more significant effect on stripe formation
than expressed in theory. To confirm this, I repeated the experiments in cells with different in-plane anchoring
strength in the cell surface: this led to a reduction in stripe wavenumber. The ease of rotation, as captured in a
modified effective cell thickness, could be incorporated into the theory, but again, we found that the experimental
result contradicted predictions. It is clear that the ease of rotation of the director has a greater effect than theanisotropy of the polymer chain.
Both experimental results compared to existing theory leads me to believe that the contribution of the elasticityof the liquid crystal is larger than that expected in theory.
References[1] M. Warner, and E.M. Terentjev, “Liquid crystal elastomers” (Oxford university press, Oxford, 2003).
[2] G, Meng, doctoral thesis, Brandeis University (2004).

Theoretical Study of Invertible States Using Matrix
Product States
YITP Shuhei Ohyama
Abstract
The Berry phase, introduced by Michael V. Berry in 1984, has been widely applied in the definition of
topological invariants, inspired by the trend of topological phases originating from quantum Hall systems.
We discussed the formulation of higher Berry phases in 1+1-dimensional systems. Specifically, by
employing the matrix product state, we define the inner product for three states and demonstrate how thisquantity provides a natural definition of the higher Berry phase. © 2023 Department of Physics, Kyoto University
An invertible state refers to a generic term for states with short-range correlations that are
realized as the ground state of a unique gapped Hamiltonian. Under appropriate symmetries,
invertible states exhibit non-trivial quantum phases, which are referred to as Symmetry-Protected
Topological (SPT) phases. It is also known that considering a family of invertible states gives
rise to topological transport phenomena similar to the Thouless pump. The invertible phase, thatis, the phase constituted by invertible states, is known to have a rich structure and has been
actively researched in the contexts of condensed matter physics, quantum information theory,
particle physics, and mathematical physics.
Such topological phases arise because the space formed by all invertible states possesses a
non-trivial topology. Therefore, by defining topological invariants for families of invertible
states, it is possible to provide a unified classification for SPT phases and the classificationof Thouless-like pump phenomena. However, aside from special cases such as free fermion systems,
no method for constructing such invariants had been known.
A crucial quantity in constructing the invariants is the Berry phase. However, when naively
calculating the Berry phase for high-dimensional many-body Hamiltonians, a divergence problem
arises in the thermodynamic limit, necessitating an appropriate generalization of the definitionof the Berry phase. To address this, we used a Matrix Product State (MPS) representation.
As a result, by employing formulations known as fermionic MPS and G-injective MPS, we discovered
invariants that characterize the fermion parity pump and G-charge pump. In particular, using
these, we demonstrated that the fermion parity pump, known to exist in free fermion systems,
is stable under interactions [1].
Furthermore, by using injective MPS, we defined a generalization of the Berry phase in 1+1
dimensional systems as an overlap of three quantum states. We showed that by integrating this,invariants for the family can be extracted [2,3,4].
[1] Shuhei Ohyama, Ken Shiozaki, and Masatoshi Sato, Phys. Rev. B 106, 165115[2] Shuhei Ohyama, Yuji Terashima, Ken Shiozaki, arXiv:2303.04252.
[3] Shuhei Ohyama, Shinsei Ryu, arXiv:2304.05356.
[4] Ken Shiozaki, Niclas Heinsdorf, Shuhei Ohyama, arXiv:2305.08109.

Luminescence fine structure and exciton–phonon interactions
in single halide perovskite nanocrystals
Optical Materials Science Group

Kenichi Cho

Abstract We studied photoluminescence spectra of single perovskite nanocrystals at low
temperatures. We observed the luminescence fine structure and determined its origin and thestrength of exciton–phonon coupling. We found that the exciton–phonon coupling is strongly
affected by the spatial overlap of electron and hole wavefunctions.
© 2023 Department of Physics, Kyoto University

Lead halide perovskites ABX3 (A = Cs, MA (CH3NH3), FA (HC(NH2)2), B = Pb, and X = Cl, Br, I) are a newclass of direct bandgap semiconductors. They possess excellent optical properties such as large absorption
coefficients, high photoluminescence (PL) quantum yields, and long carrier lifetimes, which are suitable for
optoelectronics applications [1]. Halide perovskite nanocrystals (NCs) have a well-defined cubic shape with anarrow size distribution [2]. Quantum confinement effects in NCs increase the PL quantum efficiency withkeeping the superior materials properties of their bulk counterparts. Thus, halide perovskite NCs have attracted
worldwide attention as materials for light-emitting diodes and lasers.
In this study, we examine the PL spectra of single CsPbBr3 and FAPbBr3 NCs by single-dot spectroscopy anddiscuss the origin of the luminescence fine structure in the perovskite NCs. The measurements were performed at
low temperatures, where the narrow PL linewidth of single NCs is suited to study the luminescence fine structureof NCs. The PL linewidth of all inorganic CsPbBr3 NCs was observed to be narrower than that oforganic-inorganic hybrid FAPbBr3 NCs. In addition, the PL spectra in CsPbBr3 NCs have different exciton peakstructures and can be characterized by structures with one, two, or three exciton peaks, reflecting the bright triplet
excitons in the perovskite NCs [3,4]. Several PL peaks appear in the low energy side of the strong exciton peaks.
From the size-dependence of the peak energies and the excitation fluence dependence of the PL intensities, weclarified that the low-energy PL peaks originate from trions, biexcitons, and longitudinal optical (LO) phonon
replicas of exciton PL. The binding energies of trions and biexcitons increase with decreasing NC size. The LO
phonon energies are independent of NC size, but the Huang–Rhys factor of excitons, i.e., the strength of theexciton–phonon coupling, drastically increases with decreasing NC size. We concluded that the Huang–Rhysfactor reflects the spatial overlap of the electron and hole wavefunctions inside the NCs [3,4]. The temperaturedependence of the PL linewidth was also measured from 5.5 to 200 K. The temperature-dependent broadening of
the PL linewidth is mainly determined by the Fröhlich interaction between excitons and LO phonons. The
exciton–LO-phonon coupling constant and effective LO phonon energy show no changes even when thetemperature is varied across the orthorhombic-tetragonal crystal phase transition temperature. These results
demonstrate that the exciton–phonon coupling in the perovskite NCs are not affected by the differences in crystal
structures [5].
References[1] Y. Kanemitsu and T. Handa, Jpn. J. Appl. Phys. 57, 090101 (2018).
[2] L. Protesescu et al., Nano Lett. 15, 3692 (2015).
[3] K. Cho et al., Nano Lett. 22, 7674 (2022).
[4] K. Cho et al., Nano Lett. 21, 7206 (2021).
[5] K. Cho et al., J. Chem. Phys. 158, 201104 (2023).

Impact of intraband transitions
in high-order harmonic generation from solids
Optical Materials Science Group

Kotaro Nakagawa

Abstract We have studied nonlinear coupling between intraband and interband transitions inhigh-order harmonic generation (HHG). By observing HHG from semiconductor nanocrystals withdifferent diameters, we concluded that intraband transitions with discrete electronic states
determine the size-dependent HHG intensity.
© 2023 Department of Physics, Kyoto University

The recent development of laser technology has made it possible to generate optical pulses with high electricfield strength reaching the magnitude of the Coulomb field between an electron and an atomic nucleus in solids.
Such intense laser pulses have provided opportunities to investigate completely new phenomena, and have been
attracting intensive studies on strong-laser-field physics. One of the most important nonlinear phenomena is
high-order harmonic generation (HHG), where the fundamental light with a frequency  generates its harmonics,
i.e., higher energy lights with frequencies of n (n is integer). HHG is attracting great interest as a novel lightsource in the extreme ultraviolet region, which enables attosecond pulse generation. To realize highly efficient
HHG, intraband and interband transitions in solids have been intensively studied [1,2]. The former corresponds tothe intraband acceleration of carriers driven by a laser electric field; the latter corresponds to the optical excitationof carriers between the conduction and valence bands. However, previous experiments have been unable to clarify
how these two transitions affect HHG. To achieve high-efficiency HHG, it is indispensable to gain deeper insight
into the role of these two transitions.
In this study, we focused on HHG from semiconductor nanocrystals, whose electronic structure can bechanged from discrete to continuous by controlling the nanocrystal size. This tunability of the electronic structure
makes nanocrystals well-suited for manipulating the intrabandtransitions. HHG from CdSe nanocrystal thin films was observed
under mid-infrared pulse excitation. Figure 1(a) compares HHG
spectra from CdSe nanocrystals with diameters of 2.8 and 3.8 nm.
The odd harmonics between the 7th and 13th orders are clearlyobserved for the larger nanocrystals. We observed for the smaller
nanocrystals that the HHG intensities are weaker at every
harmonic order. In Fig. 1(b), we plot the dependence of the 7th
harmonic intensity from CdSe nanocrystals against thenanocrystal diameter. It can be seen that as the nanocrystal
diameter is decreased, the HHG intensity is rapidly suppressed atdiameters around 2.5 nm. This drastic change can be explainedby the increase in the gap between discrete energy levels
originating from the quantum confinement effect (Fig. 1(b), inset)[3].
References[1] S. Ghimire et al., Nat. Phys. 7, 138 (2011).
[2] K. Nakagawa et al., Phys. Rev. Mater. 5, 016001 (2021).
[3] K. Nakagawa et al., Nat. Phys. 18, 874 (2022).

Fig. 1: (a) HHG spectra of CdSe nanocrystals.
(b) Diameter dependence of the 7th harmonic
intensity of CdSe nanocrystals. The inset
shows energy-level diagram of nanocrystals.

Bulk-boundary correspondence in non-Hermitianpoint-gap topological phases
Yukawa Institute for Theoretical Physics,

Daichi Nakamura

Abstract We establish the bulk-boundary correspondence in topological phases that are intrinsic to
non-Hermitian systems. As an application, we propose experimental platforms for these novel phases bycoupling Hermitian topological insulators/superconductors to the environment.
© 2023 Department of Physics, Kyoto University

There is a growing interest in the study of nonequilibrium physics. Among current trends, one of the noteworthy
areas of research is the exploration of band topology in non-Hermitian systems. A remarkable characteristic of
non-Hermitian systems is the existence of two distinct types of topological phases [1,2]. One type generalizes
Hermitian topological phases, while the other is intrinsic to non-Hermitian systems, referred to as "line-gap
topological phases" and "point-gap topological phases," respectively. While the bulk-boundary correspondence[3], in which bulk topological invariants count the number of gapless boundary states, is a fundamental principle
in the former phases, topological phenomena in the latter have remained unclear. This issue stems from a novel
boundary phenomenon with no Hermitian counterparts known as the non-Hermitian skin effect [4], where asignificant number of bulk states become localized at the boundary. Although previous studies have shown thatspecific 1D point-gap topologies initiate this effect [5,6], understanding the precise phenomena linked topoint-gap topological phases in each symmetry class and dimension has largely remained elusive. Furthermore, it
has been uncertain whether the bulk-boundary correspondence exists in point-gap topological phases.
In this talk, we reveal the corresponding phenomena in certain symmetry classes, specifically AZ† symmetry
classes, and establish a theory of the bulk-boundary correspondence in point-gap topological phases [7]. As anapplication of our theory, we also discuss that Hermitian topological insulators/superconductors could implement
point-gap topology by coupling to the environment [8].
References[1] Z. Gong et al., Phys. Rev. X 8, 031079 (2018).
[2] K. Kawabata et al., Phys. Rev. X 9, 041015 (2019).
[3] Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
[4] S. Yao and Z. Wang, Phys. Rev. Lett. 121, 086803 (2018).
[5] N. Okuma et al., Phys. Rev. Lett. 124, 086801 (2020).
[6] K. Zhang et al., Phys. Rev. Lett. 125, 126402 (2020).
[7] D. Nakamura, T. Bessho, and M. Sato, arXiv:2205.15635.
[8] D. Nakamura, K. Inaka, N. Okuma, and M. Sato, arXiv:2304.08110, to appear in Phys. Rev. Lett. (2023).

Topology and Strong correlation effect of Hidden symmetry
breaking superconductor
Condensed Matter Theory Group

Kosuke Nogaki

Abstract Hidden symmetry breaking has been attracted much attention due to the discovery of CeRh2As2.
In this work, we clarified topological property and the role of strong correlation effect of this heavy
fermion compound. We also investigated a novel mechanism of the field-induced superconductivity.
© 2023 Department of Physics, Kyoto University

Symmetry stands as a pivotal concept in modern physics. In heavy fermion systems, there is an inherent hidden
symmetry breaking tied to their crystalline structure. When combined with spin-orbit coupling, this hidden
symmetry breaking influences the electronic band structure. The discovery of the multi-phase superconducting
diagram in CeRh2As2 has carved a new path for exploration [1]. While foundational theories surrounding themulti-phase diagram have been suggested for over a decade [2], deeper research into topological properties andthe effects of strong correlations has been keenly anticipated. In our study, we shed light on these facets ofCeRh2As2, and we present a theoretical proposal on field-induced superconductivity unique to superconductors
with hidden symmetry breaking. Detailed summaries of each aspect of our study are presented below.
1. Topological crystalline superconductivity in locally noncentrosymmetric CeRh2As2 [3]Firstly, we elucidated the topological superconductivity in CeRh2As2. Assuming an odd-parity state in thehigh-field superconducting phase, we derived a Fermi-surface formula for Z2 invariants [4]. These invariants
specify the topological crystalline superconductivity, which is protected by the nonsymmorphic glide symmetry.
Secondly, we performed a first-principles calculation on the electronic structure of CeRh2As2. By integrating theseresults, we evaluated the Z2 invariants and identified the presence of topological superconductivity.
2. Even-odd parity transition in strongly correlated locally noncentrosymmetric superconductors: Application
to CeRh2As2 [5]While there are qualitative similarities between the weak-coupling theory [2] and the experimental results [1],inconsistencies exist. Specifically, the parity transition field derived from the theory is smaller by a factor of five.
We have delved into the effects of strong correlations in CeRh2As2. Our findings indicate an XY-type magnetic
fluctuation, aligning with recent NMR measurements [6]. Moreover, our theoretical results reveal that the parity
transition field is considerably augmented due to electron correlation effects
3. Field-induced superconductivity mediated by odd-parity multipole fluctuation [7]We concentrate on the importance of inter-sublattice hopping, which supports odd-parity multipole fluctuation.
Under the magnetic field, sublattice antisymmetric pairing is stabilized by odd-parity multipole fluctuation. This,in turn, amplifies the stability of the odd-parity superconducting state. Consequently, the field reentrant
superconducting phase diagram can be attained. The aforementioned mechanism is an exclusive characteristic ofstrongly correlated electron systems. This discovery could furnish a new approach to comprehending exotic heavy
fermion superconductors, such as UTe2 and UCoGe.
References[1] S. Khim et al., Science 373, 1012 (2021).
[2] T. Yoshida, M. Sigrist, and Y. Yanase, Phys. Rev. B 86, 134514 (2012).
[3] K. Nogaki, A. Daido, J. Ishizuka, and Y. Yanase, Phys. Rev. Research 3, L032071 (2021).
[4] M. Sato, Phys. Rev. B 81, 220504(R) (2010).
[5] K. Nogaki and Y. Yanase, Phys. Rev. B 106, L100504 (2022).
[6] S. Kitagawa et al., J. Phys. Soc. Jpn. 91, 043702 (2022).
[7] K. Nogaki and Y. Yanase, in preparation.

Quantum algorithm for persistent Betti numbers andtopological data analysis
YITP, Quantum Information

Ryu Hayakawa

Abstract Topological data analysis (TDA) is an emergent field of data analysis based on computational
topology. In TDA, computation of the persistent Betti numbers plays a central role. We present a firstquantum algorithm for estimating the normalized persistent Betti numbers, which is exponentially fasterthan the known best classical algorithm.
© 2023 Department of Physics, Kyoto University

Quantum computing is believed to outperform classical computing. It is crucial tounderstand in what applications quantum computing offers speedups and machine learning
tasks are thought to be such promising applications of quantum computing. In classicalcomputing, there is an emergent and rapidly growing field of data analysis called
the Topological Data Analysis (TDA). TDA reveals the “shape of the data” throughgeometrical and topological analysis based on the mathematical framework called persistenthomology. A crucial property of persistent homology, which is favorable in practicalsituations, is its stability against the noise concerning how the data is generated.
However, classical algorithms do not work efficiently in the high-dimensional regime of TDA
because there can be exponentially many elements that would contribute to the topology. To
overcome this limitation, Lloyd et al.[1] first provided a quantum algorithm for estimating
the normalized Betti numbers, which represent the number of (high-dimensional) holes of thedata. However, there has been no known quantum algorithm for estimating
the persistent Betti numbers, which are the central topological invariants used in TDA
based on persistent homology.
In this work, we show a first quantum algorithm that can estimate the normalized
persistent Betti numbers of arbitrary dimensions[2]. Our quantum algorithm is exponentiallyfaster than the known best classical algorithm. Moreover, there is evidence for the
exponential quantum advantage based on acomputational complexity-theoretic assumption[3].
Our quantum algorithm is based on a positivesemidefinite hermitian operator called thepersistent Laplacian. We estimate the normalized
persistent Betti numbers by the estimation of thelow-energy density of the persistent Laplacian.
Figure 1 shows a quantum circuit for the quantum
algorithm. We believe that our work opens a wide
Figure 1. Quantum circuit for estimating thepossibility of application of quantum computing"! is a unitary for
persistent Betti numbers. 𝑈
for data analysis and machine learning based on"" is a unitary encodingstate preparation and 𝑈
the complex topology of the data.
of the projector onto the ground space of thepersistent Laplacian.

References[1] S. Lloyd, S. Garnerone, and P. Zanardi., Nat. comm. 7.1 (2016): 10138.
[2] RH, Quantum 6 (2022): 873.
[3] C. Gyurik, C. Cade, and V. Dunjko. Quantum 6 (2022): 855.

Stability of Symmetry-Protected Topological Phases
as Resources of Measurement-Based Quantum Computation
Physics of Matter: Condensed Matter Physics (YITP)

Riku Masui

Abstract We study the stability of symmetry-protected topological phases from the quantum
informational viewpoint. The gate fidelity of the measurement-based quantum computation, whichquantifies how robust edge states are against quantum noises, provides us with a new insight into theclassification of the decohered SPT phases in open quantum systems.
© 2023 Department of Physics, Kyoto University

The Haldane phase, which includes the one-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) state, serves as aprime example of the symmetry-protected topological (SPT) phases. In one-dimensional quantum systems, SPTphases are distinguished from trivial ones by, e.g., finite string order parameters (SOPs), as well as by thedegeneracy of the entanglement spectrum, when the phases are characterized by pure states. Being characterizedby short-range entanglement, the SPT phases are applicable to measurement-based quantum computation(MBQC) [1]. This observation led us to explore the use of the MBQC gate fidelity [2] as a tool for detecting SPT
phases and studying the stability of them in open quantum systems. This approach enables us to characterize thestability of SPT phases from a quantum computational perspective.
In Ref. [3], two types of symmetries of quantum channels that can either preserve or disrupt the SPT order are
discussed, along with the calculation of SOPs. According to their findings, the dephasing noise preserves the SPT
order of the Haldane phase, whereas the depolarizing one destroys it. Motivated by these results, we conductedanalytical and numerical calculations of the gate fidelity of Z-rotation gates implemented by MBQC on the AKLT
state, which is subject to both types of noise-induced decoherence. Our results demonstrate that the behavior ofgate fidelity in response to these noises is consistent with the conclusion of Ref. [3]. Moreover, we have shownthat the gate fidelity gives us more detailed information on the classification of the decohered SPT phases
compared to the previous methods based on the SOP and other order parameters.

Fig. 1. Numerical results of the fidelity for the gate UZ(θ) = exp(-iθZ/2) against two types of noises.

References[1] G. K. Brennen and A. Miyake, Phys. Rev. Lett. 101, 010502 (2008).
[2] K. Fujii et al., Phys. Rev. Lett. 110, 120502 (2013).
[3] C. de Groot, A. Turzillo, and N. Schuch, Quantum 6, 856 (2022)

Dynamic coupling of dynamics of bilayers andBrownian motion of colloidal particles
Soft Matter Physics Laboratory

Shingo YOSHIOKA

Abstract We found “dynamic coupling” between bilayer fluctuations and colloid Brownian motion. For
lamellae, we found that the layer compression modulus was reduced because colloidal motions hinderinteractions. In contrast, in a sponge phase, the elastic Gaussian curvature modulus of the sponge was
reduced. Colloid motions reduce the stability each system.
© 2023 Department of Physics, Kyoto University

Lyotropic liquid crystals (LLCs), which are formed by an amphiphilic surfactant and water, adopt a wide
variety of structures. For some LLCs, the basic composition unit is a bilayer of surfactant molecules. Typicalbilayer phases include the lamellar phase, where bilayers spread two-dimensionally and form a layered structure,and the sponge phase, where bilayers separate the solvent into two regions and create a bicontinuous structure.
Bilayers undulate in water by thermal fluctuations. In lamellae or sponges, some bilayers interact with eachother and undergo a cooperative diffusion depending on the structure. In the lamellar phase, adjacent bilayers
collide directly: this steric interaction stabilizes lamellae. In the sponges, the positions of regions can change,
causing a local change in topology. Undulations of lamellae depend on the layer compression modulus while thetopological dynamics of sponges depend on the elastic Gaussian curvature modulus.
Mixtures of bilayers and colloidal particles exhibit a number of unique phenomena due to interactions between
its components [1-2]. They focused on static characteristics or response from external field. So in this work, we
focus on “dynamical coupling” i.e. between the dynamics of bilayers and the thermal motion of colloidal particles,
using dynamic light scattering (DLS) to probe fluctuations. By studying the undulations of lamellae andtopological dynamics of sponge, distinct fluctuations originating from the same undulations of bilayer, we study
the effect of colloidal motion on the undulation of the bilayer from different points of view.
Firstly, in a mixture of lamellae and colloidal particles, theautocorrelation function from DLS always showed a single relaxation mode
corresponding to undulations of lamellae in mixture. We found that themode slows down monotonically with increasing colloid concentration Φ(Fig. 1). Colloidal motions are coupled with undulations of lamellae, suchthat adjacent lamellar bilayers collide direct each other by undulations.
Then colloidal motions inhibit the direct lamellar collisions and reduce thelayer compression modulus.
Next, in a mixture of sponges and colloidal particles, a single mode
Fig. 1 Diffusion coefficient vs.
corresponding to topological fluctuations of the sponge phase was observed. colloid concentration Φ in a mixture
Unlike for lamellae, the topological dynamics of the sponge becomes faster of lamellae and colloidal particles.
when more colloidal particles are introduced (Fig. 2). This means thatcolloidal motions help crumple the membrane and reduce the elastic
Gaussian curvature modulus.
In each case, colloidal motions reduce the moduli by colliding with
undulating bilayers. These moduli stabilize the phase respectively, so
colloidal motions reduce the stability of the phase.
References
Fig. 2 Diffusion coefficient vs.
[1] J. Yamamoto and H. Tanaka. Nat. Mater., 4, 75 (2005).
colloid
concentration Φ in a mixture[2] H. Tanaka, M. Isobe, and J. Yamamoto. Phys. Rev. Lett., 16, 89 (2002).
of sponges and colloidal particles.