Identifying Topological Order by Entanglement Entropy

TL;DR

This paper presents a practical DMRG-based method to identify topological phases by calculating Topological Entanglement Entropy with high accuracy, demonstrated on various models including a kagome lattice spin liquid.

Contribution

It introduces a novel approach using DMRG to accurately compute TEE, explaining the natural emergence of minimally entangled states and confirming topological order in complex models.

Findings

Successfully calculated TEE with 10^{-3} accuracy on several models.

Confirmed the quantum kagome antiferromagnet as a topological spin liquid.

Provided a practical method for identifying topological phases in realistic systems.

Abstract

Topological phases are unique states of matter incorporating long-range quantum entanglement, hosting exotic excitations with fractional quantum statistics. We report a practical method to identify topological phases in arbitrary realistic models by accurately calculating the Topological Entanglement Entropy (TEE) using the Density Matrix Renormalization Group (DMRG). We argue that the DMRG algorithm naturally produces a minimally entangled state, from amongst the quasi-degenerate ground states in a topological phase. This proposal both explains the success of this method, and the absence of ground state degeneracy found in prior DMRG sightings of topological phases. We demonstrate the effectiveness of the calculational procedure by obtaining the TEE for several microscopic models, with an accuracy of order $10^{-3}$ when the circumference of the cylinder is around ten times the correlation length. As an example, we definitively show the ground state of the quantum $S=1/2$ antiferromagnet on the kagom\'e lattice is a topological spin liquid, and strongly constrain the full identification of this phase of matter.