Simulation of ring-exchange models with projected entangled pair states

Abstract

Algorithms to simulate ring-exchange models on a square lattice using projected entangled pair states (PEPSs) 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 of the environment. To understand the numerical instability during 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.