Simulation of the Ring-exchange Models with Projected Entangled Pair States

TL;DR

This paper develops algorithms using projected entangled pair states (PEPS) to simulate ring-exchange models, improving optimization stability and benchmarking with accurate results on topological and chiral order properties.

Contribution

It introduces a generalized imaginary time evolution method for PEPS with ring interactions and a regulation procedure to reduce numerical singularity, enhancing simulation accuracy.

Findings

Accurate ground state energies for the toric code model.

Identification of strong vector chiral order in the cyclic ring exchange model.

Effective reduction of PEPS singularity improves numerical stability.

Abstract

Algorithms to simulate the ring-exchange models using the projected entangled pair states (PEPS) are developed. We generalize the imaginary time evolution (ITE) method to optimize PEPS wave functions for the models with ring-exchange interactions. We compare the effects of different approximations to the environment. To understand the numerical instability during the optimization, we introduce the ``singularity'' of a PEPS and develop a regulation procedure that can effectively reduce the singularity of a PEPS. We benchmark our method with the toric code model, and obtain extremely accurate ground state energies and topological entanglement entropy. We also benchmark our method with the two-dimensional cyclic ring exchange model, and find that the ground state has a strong vector chiral order. The algorithms can be a powerful tool to investigate the models with ring interactions. The methods developed in this work, e.g., the regularization process to reduce the singularity can also be applied to other models.