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

TL;DR

This paper introduces and benchmarks isometric tensor network states (isoTNSs) for simulating 2D quantum spin systems, demonstrating efficient real-time evolution and ground state calculations with applications to the Ising and Kitaev models.

Contribution

The paper develops isoTNS-based algorithms, including TEBD² and DMRG², for efficient simulation of 2D quantum systems, extending tensor network methods to higher dimensions.

Findings

Accurate computation of dynamical spin structure factors for 2D models.

Comparison of isoTNS results with spin-wave theory and exact solutions.

Demonstration of efficient simulation techniques for complex quantum systems.

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.