Tensor-entanglement renormalization group approach to 2D quantum systems

TL;DR

This paper introduces a tensor network-based variational approach using tensor entanglement renormalization group to study complex 2D quantum phases with long-range entanglement, including topological states.

Contribution

It develops a novel 2D real space RG algorithm with tensor product states for analyzing long-range entangled quantum phases.

Findings

Successfully applied to 2D quantum spin models

Able to handle topological and long-range entangled phases

Provides a new computational tool for 2D quantum systems

Abstract

Traditional mean-field theory is a simple generic approach for understanding various phases. But that approach only applies to symmetry breaking states with short-range entanglement. In this paper, we describe a generic approach for studying 2D quantum phases with long-range entanglement (such as topological phases). Our approach is a variational method that uses tensor product states (also known as projected entangled pair states) as trial wave functions. We use a 2D real space RG algorithm to evaluate expectation values in these wave functions. We demonstrate our algorithm by studying several simple 2D quantum spin models.