Accurate determination of tensor network state of quantum lattice models in two dimensions

TL;DR

This paper introduces a new numerical method for accurately computing ground state properties of two-dimensional quantum lattice models using tensor-network wave functions, employing a projection approach with Trotter-Suzuki decomposition and coarse-grain renormalization.

Contribution

The authors develop a novel tensor network projection method that efficiently handles high bond dimensions in 2D models, improving accuracy and scalability in the thermodynamic limit.

Findings

Accurately computes ground state energy and magnetization for the Heisenberg model on a honeycomb lattice.

Results agree well with quantum Monte Carlo and other established methods.

Handles tensor-network wavefunctions with high bond dimension (D=8) efficiently.

Abstract

We have proposed a novel numerical method to calculate accurately the physical quantities of the ground state with the tensor-network wave function in two dimensions. We determine the tensor network wavefunction by a projection approach which applies iteratively the Trotter-Suzuki decomposition of the projection operator and the singular value decomposition of matrix. The norm of the wavefunction and the expectation value of a physical observable are evaluated by a coarse grain renormalization group approach. Our method allows a tensor-network wavefunction with a high bond degree of freedom (such as D=8) to be handled accurately and efficiently in the thermodynamic limit. For the Heisenberg model on a honeycomb lattice, our results for the ground state energy and the staggered magnetization agree well with those obtained by the quantum Monte Carlo and other approaches.