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arXiv · 2112.08394

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

Sheng-Hsuan Lin·Michael Zaletel·Frank Pollmann
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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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Sheng-Hsuan Lin, Michael Zaletel, Frank Pollmann. 2021-12-15. Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks. https://doi.org/10.1103/physrevb.106.245102

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