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.

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

References in corpus (16)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Real time evolution using the density matrix renormalization group
• Matrix product states represent ground states faithfully
• Tensor renormalization group approach to 2D classical lattice models
• Entropy scaling and simulability by Matrix Product States
• Minimally Entangled Typical Thermal State Algorithms
• Algorithms for finite Projected Entangled Pair States
• Compactly-supported Wannier functions and algebraic $K$-theory
• Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR lineshape
• Chiral topological spin liquids with projected entangled pair states
• Chiral projected entangled-pair state with topological order
• Fermionic Implementation of Projected Entangled Pair States Algorithm
• Sequentially generated states for the study of two dimensional systems
• Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model
• Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space

Cited by in corpus (22)

• A density-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelity
• Gauging tensor networks with belief propagation
• Generating function for projected entangled-pair states
• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• 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
• Spectral functions with infinite projected entangled-pair states
• Classical dynamics of the antiferromagnetic Heisenberg $S=1/2$ spin ladder
• Ising Meson Spectroscopy on a Noisy Digital Quantum Simulator
• Fermionic Isometric Tensor Network States in Two Dimensions
• Dual-isometric Projected Entangled Pair States
• 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
• Diagonal Isometric Form for Tensor Network States in Two Dimensions
• Sampling two-dimensional isometric tensor network states
• Single-hole spectral functions in one-dimensional quantum magnets with different ground states