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

• URL: http://arxiv.org/abs/2112.08394v2
• Date: Mon, 7 Nov 2022 02:37:33 GMT
• Title: Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
• Authors: Sheng-Hsuan Lin, Michael Zaletel, Frank Pollmann
• Abstract summary: We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs) We discuss several technical details regarding the implementation of isoTNSs-based algorithms and compare different disentanglers. We compute the dynamical spin structure factor of 2D quantum spin systems for two paradigmatic models.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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