17 Monday

Ying-Jer Kao [National Taiwan University]
Symmetric tensor network studies of Kitaev spin liquids
We study the spin-1/2 star and spin-1 honeycomb Kitaev models using ℤ_2 invariant
Projected Entangled Pair States (PEPS). We find that the transition from Abelian to nonAbelian phase of the star lattice Kitaev model can be understood as charge and flux
transmuting into 𝜎 anyon in the ℤ_2 invariant PEPS framework. Besides, we show thatthe ground state always has infinite correlation length in the non-Abelian regime,
consistent with the no-go theorem that a chiral PEPS has a gapless parent Hamiltonian.
On the other hand, we confirm the ℤ_2 spin liquid nature of isotopic spin-1 Kitaev
honeycomb model by evaluating the virtual order parameters defined on the virtual
Hilbert space of the tensor network. Using the correspondence between the transfer matrix
spectrum and low-lying excitations, we find that contrary to the dispersive Majorana
excitation in the spin-1/2 case, the system has a dispersive charge anyon excitation.
Bottom of the gapped single-particle charge anon excitations are also identified with thecorresponding correlation length 𝜉≈6.7 unit cells.

Atsushi Iwaki [University of Tokyo]
Thermal pure quantum matrix product states: Sample efficiency and Random fluctuation
Thermal pure quantum matrix product state (TPQ-MPS) is a microscopic description ofa nearly pure quantum state at finite temperature based on the matrix productrepresentation with the auxiliary sites placed on the edges of the system as entanglement
bath. The state carries an entanglement entropy that follows a volume law up to the wholesystem size [1]. However, a general description of a finite temperature many-body state
often relies on the mixture of pure states where a volume-law entropy that cannot be fully
captured by a single pure state can be recovered by the classical ensemble. Although thedegree of the mixture shall have relevance to the purity of the quantum state, the measureof purity that can be applied to a general mixed state was lacking. We focus on theefficiency of the random sampling method proposed in Ref.[2], which could measure thenumber of required sample averages or the degree of mixture. By transforming theefficiency, we develop a formula that can measure the purity of the quantum many-body
mixed state explicitly by using a physically meaningful observable.
[1] A. Iwaki, A. Shimizu, and C. Hotta, PRResearch 3, L022015 (2021).
[2] S. Goto, R. Kaneko, and I. Danshita, PRB 104, 045133 (2021).

Wei Tang [Ghent University]
Continuous matrix product operator approach to finite temperature quantum states and its
application to the nonlinear sigma model with $¥theta=¥pi$ term
In the first part of our presentation, we will present a tensor network algorithm thatsimulates the one-dimensional and quasi-one-dimensional systems at the thermodynamic
limit. Using the continuous matrix product operator (cMPO) representation for thepartition function, the approach handles both short-range and long-range interactions in
the thermodynamic limit without incurring any time discretization error. Besides ordinary
thermodynamic quantities, this approach can be used to calculate the imaginary-timecorrelation functions and local dynamical quantities, the latter of which can be observedin nuclear magnetic resonance experiments. In the second part of our presentation, we
employ the cMPO method to the $(1+1)$-dimensional $O(3)$ nonlinear $¥sigma$-modelwith $¥theta=¥pi$ term. Within the Hamiltonian formulation, this field theory emerges as
the finite-temperature partition function of a modified quantum rotor model decorated
with magnetic monopoles. Using the monopole harmonics basis, we derive the matrix
representation for this modified quantum rotor model, which enables tensor network
simulations. Using the cMPO method, we study the finite-temperature properties of thismodel and reveal its massless nature. The central charge as a function of the coupling
constant is directly extracted in our calculations and compared with field theory
predictions.

Lei Wang [Institute of Physics, Chinese Academy of Science]
Neural canonical transformation for m* of two-dimensional electron gas
The quasiparticle effective mass m* of interacting electrons is a fundamental quantity in
the Fermi liquid theory. However, the precise value of the effective mass of uniform
electron gas is still elusive after decades of research. The newly developed neuralcanonical transformation approach [Xie et al., 2105.08644] offers a principled way to
extract the effective mass of electron gas by directly calculating the thermal entropy at
low temperature. The approach models a variational many-electron density matrix using
two generative neural networks: an autoregressive model for momentum occupation anda normalizing flow for electron coordinates. Our calculation reveals a suppression ofeffective mass in the two-dimensional spin-polarized electron gas, which is more
pronounced than previous reports in the low-density strong-coupling region. Thisprediction calls for verification in two-dimensional electron gas experiments.
Ref: Hao Xie, Linfeng Zhang, Lei Wang, arXiv:2201.03156

18 Tuesday

Ian McCulloch [University of Queensland]
Exponents and Scaling at Dynamical Quantum Critical Points
A Dynamical Quantum Critical Point (DQPT) is a relatively recent notion whereby a
global quench of a quantum state induces a sequence of critical points (meaning nonanalytic behaviour of the boundary partition function) as a function of time. I will
present an algorithm for calculating the higher moments of the Loschmidt Echo for atranslationally invariant infinite MPS and show how it can be used to probe universal
behaviour of DQPTs, focussing on the phase of the Loschmidt Amplitude, which has beensomewhat neglected in the past.

Kevin Slagle [Caltech]
Fast Tensor Disentangling Algorithm andStochastic Tensor Network

Emergent Quantum Mechanics from a

In the first part of this talk, I describe a fast non-iterative algorithm to approximately
disentangle a tensor. I also provide pictorial intuition, demonstrate the algorithm's
usefulness with numerical experiments, and mention future directions.
(arXiv:2104.08283) In the second part, we use tensor networks to demonstrate that it ispossible for quantum mechanics to emerge from classical mechanics. In particular, using
a well-controlled perturbation theory and numerical simulations, we show that the time
evolution of any quantum mechanics Hamiltonian can be realized at the boundary of astochastic tensor network with local dynamics.

Saeed Jahromi[Institute for Advanced Studies in Basic Sciences (IASBS)]
Graph-based projected entangled-pair state for any infinite lattice
We present a general graph-based Projected Entangled-Pair State (gPEPS) algorithm toapproximate both ground states and thermal states of nearest-neighbor local Hamiltonians
on any lattice or graph of infinite size. By introducing the structural-matrix which codifies
the details of tensor networks on any graphs in any dimension d, we are able to produce
a code that can be essentially launched to simulate any lattice. We further introduce an
optimized algorithm to compute simple tensor updates as well as expectation values andcorrelators with a mean-field-like effective environments for both zero- and finitetemperature. Though not being variational, this strategy allows to cope with PEPS of verylarge bond dimension (e.g., D=100), and produces remarkably accurate results in thethermodynamic limit in many situations, and specially when the correlation length issmall and the connectivity of the lattice is large. We present several benchmarck results
to show the accuracy and efficiency of our methods.

Henrik Dreyer [Cambridge Quantum]
Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks
We study the response of critical Resonating Valence Bond (RVB) spin liquids to dopingwith longer-range singlets, and more generally of U(1)-symmetric tensor networks to
non-symmetric perturbations. Using a field theory description, we find that in the RVB,
doping constitutes a relevant perturbation which immediately opens up a gap, contrary toprevious observations. Our analysis predicts a very large correlation length even at
significant doping, which we verify using high-accuracy numerical simulations. Thisemphasizes the need for careful analysis, but also justifies the use of such states as avariational ansatz for critical systems. Finally, we give an example of a PEPS where nonsymmetric perturbations do not open up a gap and the U(1) symmetry re-emerges.
Based on https://arxiv.org/abs/2008.04833

Chia-Min Chung [National Sun Yat-Sen University]
Stripes and superconductivity in the two-dimensional Hubbard model
The two-dimensional (2D) Hubbard model is a fundamental model in understanding
superconductivity in cuprates. By implying density matrix renormalization group andquantum Monte Carlo methods, we carefully study the ground state properties of 2D
Hubbard model and t'-Hubbard model. We especially focus on the so-called stripe order,
and its competition to superconductivity.

19 Wednesday

Ryui Kaneko [Kindai University]
Tensor-network study of correlation-spreading dynamics in two-dimensional systems
We analyze real-time dynamics of the two-dimensional Bose-Hubbard model after asudden quench starting from the Mott insulator by means of the two-dimensional tensornetwork method [R. Kaneko and I. Danshita, arXiv:2108.11051].Calculated singleparticle correlation functions are found to be in good agreement with a recent experiment[Y. Takasu et al., Sci. Adv. 6, eaba9255 (2020)], which cross validates the experiment andthe numerical simulation. By estimating the phase and group velocities from the singleparticle and density-density correlation functions, we predict how these velocities vary inthe moderate interaction region, which will be useful for future experiments. If timeallows, we will also discuss the quench dynamics of the two-dimensional quantum Isingmodel recently realized in the Rydberg atom arrays.

Masazumi Honda [Yukawa Institute]
Digital quantum simulation of higher-charge Schwinger model with topological term
I am going to talk about application of quantum computation to numerical simulation ofquantum field theory. Specifically, we implement a digital quantum simulation of a gauge
theory with a topological term in Minkowski spacetime, which is practically inaccessible
by standard lattice Monte Carlo simulations. We focus on 1+1 dimensional quantum
electrodynamics with a topological term and a charge-q Dirac fermion known as the
Schwinger model. We construct the true vacuum state of a lattice Schwinger model using
adiabatic state preparation which, in turn, allows us to compute an expectation value ofthe fermion mass operator with respect to the vacuum. Upon taking a continuum limit wefind that our result in massless case agrees with the known exact result. In massive case,
we find an agreement with mass perturbation theory in small mass regime and deviations
in large mass regime. We also study a potential between heavy charged particles and seethat the potential changes its qualitative behavior as changing parameters: it shows
confinement, screening and an exotic behavior called negative tension behavior in which
particles with opposite charges repel with each other.
[1]

B.Chakraborty, M. Honda, T. Izubuchi, Y. Kikuchi and A. Tomiya,arXiv:2001.00485[2] M. Honda, E. Itou, Y. Kikuchi, L. Nagano and T. Okuda, arXiv:2105.03276[3] M. Honda, E. Itou, Y. Kikuchi and Y. Tanizaki arXiv:2110.14105

Yang Liu [Institute of Physics, Chinese Academy of Sciences]
Numerical research of excitations of two dimensional magnetic lattice based on PEPS

Ryotaro Suzuki [Freie Universität Berlin]
Computational power of one- and two-dimensional dual-unitary quantum circuits"Quantum circuits that are classically simulatable tell us when quantum computation
becomes less powerful than or equivalent to classical computation. Such classicallysimulatable circuits are of importance because they illustrate what makes universal
quantum computation different from classical computers. I will talk about our recent
proposal on classically simulatable circuits by making use of dual-unitary quantum
circuits, which have been recently investigated as exactly solvable models of nonequilibrium physics, and we characterize their computational power."20 Thursday

Sajant Anand [UC Berkeley]
Isometric Tensor Network States on an Infinite Strip
Contraction of standard 2D tensor network ansatzes relies on approximation schemes, as
tensor contractions costs scale exponentially with system size. Recently, the IsometricTensor Network (isoTNS) ansatz was introduced for 2D finite quantum systems on asquare lattice, allowing for exact O(1) evaluation of expectation values provided we canefficiently move the orthogonality center throughout the network. Here we generalize this
isoTNS ansatz to strip geometries, in which the networks are infinite by finite and consistof translationally invariant rows of tensors. We demonstrate several algorithms for theinfinite Moses Move (iMM), which moves the orthogonality hypersurface between
columns of infinite length in the network. Using these iMM algorithms, we perform
imaginary time evolution to identify the ground state of our 2D system, where the cost of
optimization scales linearly with strip width rather than exponentially.
Shinichiro Akiyama [Tsukuba University]
Tensor renormalization group approach to higher-dimensional lattice field theories
The tensor renormalization group (TRG) approach is a variant of the real-space
renormalization group to evaluate the path integral in the thermodynamic limit, without
resorting to any probabilistic interpretation for the given Boltzmann weight. Moreover,since the TRG can directly deal with the Grassmann variables, this approach can beformulated in the same manner for the systems with bosons, fermions, or both of them.
These advantages of the TRG approach have been confirmed by earlier studies of various(2+1)- and (3+1)-dimensional lattice theories, which suggest that the TRG potentiallyenables us to investigate the parameter regimes where it is difficult to access with thestandard stochastic numerical methods, such as the Monte Carlo simulation. In this talk,reviewing recent progress on the TRG algorithms, we explain their application to the
Hubbard model at finite density and relativistic lattice fermions.

Runze Chi [Institute of Physics，Chinese Academy of Sciences]Tensor-Network Study of the Excitation of the Triangular Lattice Antiferromagnetic XXZ
Model
We calculate the excitation spectrum of the triangular antiferromagnetic XXZ modelusing the excitation iPEPS ansatz. The simulation results show similar characteristics
with the experimental results. We find that the higher soft mode at the M point originatesfrom two magnon branches in the zero-field which has not been pointed by the previous
theory.

Hui-Ke Jin [Technische Universität München]
Matrix Product States for Hartree-Fock-Bogoliubov Wave Functions
We provide an efficient and accurate method for converting Hartree-Fock-Bogoliubov
wave functions into matrix product states (MPSs). These wave functions, also known as“Bogoliubov vacua”, exhibit a peculiar entanglement structure that the eigenvectors of
the reduced density matrix are also Bogoliubov vacua. We exploit this important feature
to obtain their optimal MPS approximation and derive an explicit formula forcorresponding MPS matrices. The performance of our method is benchmarked with the
Kitaev chain and the Majorana-Hubbard model on the honeycomb lattice. The approachfacilitates the applications of Hartree-FockBogoliubov wave functions and is ideallysuited for combining with the density-matrix renormalization group method.

Jozef Genzor [National Center for Theoretical Science, National Taiwan University]
J1-J2 Fractal by Multi-Recursion HOTRG
We develop a novel technique to investigate phase transition phenomena on self-similar
lattices constructed on a square-lattice frame with two different coupling strengths, J1 andJ2. By introducing two types of couplings, it is possible to continuously transform aregular square lattice into a fractal lattice by adjusting some couplings determined by theunderlying fractal pattern. In extreme cases, a pure fractal lattice is obtained when
specified bonds are cut by setting J2 = 0, and a regular square lattice is recovered when
J1 = J2 = 1. Besides, when J1 < J2, a different fractal pattern is obtained that is “inverse”
to the J1 > J2 case. We can perform measurements using impurity tensors in any regime,
including a pure fractal lattice and regular square lattice. Instead of having one type of
local tensor and one extension relation as in the Higher-Order Tensor Renormalization
Group (HOTRG) algorithm (Ref. [1]), we introduce several types of local tensors, witheach being extended by a different recursive relation. The recursive relations specify how
to combine different tensors to extend the system size. For concreteness, we focus on the
Ising model on fractal lattice introduced in Ref. [2] to compare with our method easily;
however, our technique can be applied to a wide variety of fractal patterns. The
computational cost scales with the bond dimension the same way as the HOTRG in two
dimensions with a constant-factor overhead.
[1] Z.Y. Xie, J. Chen, M.P. Qin, J.W. Zhu, L.P. Yang, and T. Xiang,
Phys. Rev. B 86, 045139 (2012).
[2] J. Genzor, A. Gendiar, and T. Nishino, Phys. Rev. E 93, 012141 (2016).

21 Friday

Kotaro Tamaoka [Nihon University]
Pseudo entropy and its applications
Recent studies have shown an interesting connection between tensor networks, quantum
gravity, and holography. For example, certain tensor networks can provide toy models ofholography. In this talk, we will introduce “pseudo entropy”, a holography-inspired
generalization of the entanglement entropy. After reviewing backgrounds, we will discuss
how we can find such a generalization from the viewpoint of holography. We will thendiscuss some applications to quantum many-body systems.

Rong-Yang Sun [RIKEN Center for Computational Science (R-CCS)]
Nematic quantum liquid state in the triangular-lattice SU(4) spin-orbital model
The simplest spin-orbital model can host a nematic spin-orbital liquid on the triangularlattice. We provide clear evidence that the ground state of the SU(4) Kugel-Khomskii
model on the triangular lattice can be well described by a “single” Gutzwiller projectedwave function with an emergent parton Fermi surface, despite it exhibits strong ﬁnite-size
eﬀect in quasi-one-dimensional cylinders. The ﬁnite-size eﬀect can be resolved by thefact that the parton Fermi surface consists of open orbits in the reciprocal space. Thereby,a stripy liquid state is expected in the two-dimensional limit, which preserves the SU(4)symmetry while breaks the translational symmetry by doubling the unit cell along one of
the lattice vector directions. It is indicative that these stripes are critical and the central
charge is c = 3, in agreement with the SU(4) 1 Wess-Zumino-Witten conformal ﬁeld
theory. All these results are consistent with the Lieb-Schultz-Mattis-Oshikawa-Hastings
theorem.

Roman Orus [DIPC / Multiverse Computing]News on tensor network simulations for quantum matter and beyond
In this talk I will give a brief overview of some recent developments concerning tensor
network methods for the simulation of quantum matter in my group. These include
simulations of breathing Kagome antiferromagnets, 3d thermal bosons, 3d Kitaev models
and 2d models with SU(2) symmetry.