Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks

Abstract

We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs), which generalizes the isometric conditions of the canonical form of one-dimensional matrix-product states to tensor networks in higher dimensions. We discuss several technical details regarding the implementation of isoTNSs-based algorithms and compare different disentanglers -- which are essential for an efficient handling of isoTNSs. We then revisit the time evolving block decimation for isoTNSs (${\text{TEBD}}^2$) and explore its power for real time evolution of two-dimensional (2D) lattice systems. Moreover, we introduce a density matrix renormalization group algorithm for isoTNSs (${\text{DMRG}}^2$) that allows to variationally find ground states of 2D lattice systems. As a demonstration and benchmark, we compute the dynamical spin structure factor of 2D quantum spin systems for two paradigmatic models: First, we compare our results for the transverse field Ising model on a square lattice with the prediction of the spin-wave theory. Second, we consider the Kitaev model on the honeycomb lattice and compare it to the result from the exact solution.

arXiv comment16 pages, 11 figures, 1 table (+appendix: 6 pages, 2 figure, 2 table)

References in corpus (69)

• Anyons in an exactly solved model and beyond
• The density-matrix renormalization group in the age of matrix product states
• Area laws for the entanglement entropy - a review
• Efficient classical simulation of slightly entangled quantum computations
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Efficient simulation of one-dimensional quantum many-body systems
• Real time evolution using the density matrix renormalization group
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• An Area Law for One Dimensional Quantum Systems
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Matrix product states represent ground states faithfully
• Time-evolution methods for matrix-product states
• Tensor renormalization group approach to 2D classical lattice models
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Corner Transfer Matrix Renormalization Group Method
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Entropy scaling and simulability by Matrix Product States
• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Tensor Network Renormalization
• Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes
• Sequential generation of entangled multi-qubit states
• Algorithms for entanglement renormalization
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• The computational complexity of PEPS
• Minimally Entangled Typical Thermal State Algorithms
• Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
• Differentiable Programming Tensor Networks
• Variational optimization with infinite projected entangled-pair states
• The iPEPS algorithm, improved: fast full update and gauge fixing
• Algorithms for finite Projected Entangled Pair States
• Gradient methods for variational optimization of projected entangled-pair states
• What limits the simulation of quantum computers?
• Dynamics of Fractionalization in Quantum Spin Liquids
• Isometric Tensor Network States in Two Dimensions
• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• Quantum phase transition in spin-3/2 systems on the hexagonal lattice - optimum ground state approach
• Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
• Projected entangled-pair states can describe chiral topological states
• Renormalization of tensor networks using graph independent local truncations
• A Density Matrix Algorithm for 3D Classical Models
• Compactly-supported Wannier functions and algebraic $K$-theory
• Fermionic orbital optimisation in tensor network states
• Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR lineshape
• Simulating excitation spectra with projected entangled-pair states
• A canonical form for Projected Entangled Pair States and applications
• Gauge fixing, canonical forms and optimal truncations in tensor networks with closed loops
• Riemannian optimization of isometric tensor networks
• Chiral topological spin liquids with projected entangled pair states
• Finding purifications with minimal entanglement
• Chiral projected entangled-pair state with topological order
• Gradient optimization of finite projected entangled pair states
• Isometric Tensor Network representation of string-net liquids
• Fermionic Implementation of Projected Entangled Pair States Algorithm
• Sequentially generated states for the study of two dimensional systems
• Sequential generation of projected entangled-pair states
• Algorithms for entanglement renormalization: boundaries, impurities and interfaces
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
• Local Matrix Product Operators: Canonical Form, Compression, & Control Theory
• Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model
• Accurate simulation for finite projected entangled pair states in two dimensions
• Conversion of projected entangled pair states into a canonical form
• Direct sampling of projected entangled-pair states
• Three-dimensional isometric tensor networks
• Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space
• Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles
• Hybrid infinite time-evolving block decimation algorithm for long-range multi-dimensional quantum many-body systems
• Variational Monte Carlo with the Multi-Scale Entanglement Renormalization Ansatz

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• Isometric tensor network representations of two-dimensional thermal states
• Dynamics of correlation spreading in low-dimensional transverse-field Ising models
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
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• Classical dynamics of the antiferromagnetic Heisenberg $S=1/2$ spin ladder
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• Emergent Quantum Mechanics at the Boundary of a Local Classical Lattice Model
• Sequential quantum simulation of spin chains with a single circuit QED device
• Finite-size scaling on the torus with periodic projected entangled-pair states
• TensorKrowch: Smooth integration of tensor networks in machine learning
• Two Dimensional Isometric Tensor Networks on an Infinite Strip
• Quantum Gauge Networks: A New Kind of Tensor Network
• Scalable projected entangled-pair state representation of random quantum circuit states
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