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arXiv · 2108.06856

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

Chao Wang·Shaojun Dong·Yongjian Han·Lixin He
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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.

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Chao Wang, Shaojun Dong, Yongjian Han, Lixin He. 2021-08-16. Simulation of the Ring-exchange Models with Projected Entangled Pair States. https://doi.org/10.1103/physrevb.105.024417

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