Accurate simulation for finite projected entangled pair states in two dimensions

TL;DR

This paper introduces a novel tensor-network algorithm based on variational Monte Carlo sampling that significantly enhances the simulation of two-dimensional quantum lattice models, enabling larger system sizes and improved accuracy.

Contribution

The authors develop an efficient 2D tensor-network method utilizing Monte Carlo sampling, allowing for larger system simulations and better accuracy than previous approaches.

Findings

Successfully simulated 32x32 square-lattice antiferromagnetic Heisenberg model.

Achieved high accuracy in ground state energy and spin correlations.

Method outperforms traditional tensor network techniques in finite systems.

Abstract

Based on the scheme of variational Monte Carlo sampling, we develop an accurate and efficient two-dimensional tensor-network algorithm to simulate quantum lattice models. We find that Monte Carlo sampling shows huge advantages in dealing with finite projected entangled pair states, which allows significantly enlarged system size and improves the accuracy of tensor network simulation. We demonstrate our method on the square-lattice antiferromagnetic Heisenberg model up to $32 \times 32$ sites, as well as a highly frustrated $J_1-J_2$ model up to $24\times 24$ sites. The results, including ground state energy and spin correlations, are in excellent agreement with those of the available quantum Monte Carlo or density matrix renormalization group methods. Therefore, our method substantially advances the calculation of 2D tensor networks for finite systems, and potentially opens a new door towards resolving many challenging strongly correlated quantum many-body problems.