Tensor-entanglement renormalization group approach as a unified method for symmetry breaking and topological phase transitions

Abstract

Traditional mean-field theory is a generic variational approach for analyzing symmetry breaking phases. However, this simple approach only applies to symmetry breaking states with short-range entanglement. In this paper, we describe a generic approach for studying two-dimensional (2D) quantum phases with long-range entanglement (such as topological phases). The method is based on (a) a general class of trial wave functions known as tensor-product states and (b) a 2D real-space renormalization group algorithm for efficiently calculating expectation values for these states. We demonstrate our method by studying several simple 2D quantum spin models exhibiting both symmetry breaking phase transitions and topological phase transitions. Our approach can be viewed as a unified mean-field theory for both symmetry breaking phases and topological phases.