Topological phases and topological entropy of two-dimensional systems with finite correlation length

TL;DR

This paper investigates the topological entropy in two-dimensional quantum systems with finite correlation length, analyzing models like the quantum eight-vertex, quantum dimer, and Kitaev wave functions to understand boundary effects and phase stability.

Contribution

It introduces simplified methods to compute topological entropy and examines how finite correlation length influences topological features across various models.

Findings

Finite correlation length introduces boundary-related corrections to topological entropy.

Topological entropy is determined by non-trivial loop configurations in the ground state.

Extensions of Kitaev's wave function reveal the stability of topological phases against charge fluctuations.

Abstract

We elucidate the topological features of the entanglement entropy of a region in two dimensional quantum systems in a topological phase with a finite correlation length $\xi$. Firstly, we suggest that simpler reduced quantities, related to the von Neumann entropy, could be defined to compute the topological entropy. We use our methods to compute the entanglement entropy for the ground state wave function of a quantum eight-vertex model in its topological phase, and show that a finite correlation length adds corrections of the same order as the topological entropy which come from sharp features of the boundary of the region under study. We also calculate the topological entropy for the ground state of the quantum dimer model on a triangular lattice by using a mapping to a loop model. The topological entropy of the state is determined by loop configurations with a non-trivial winding number around the region under study. Finally, we consider extensions of the Kitaev wave function, which incorporate the effects of electric and magnetic charge fluctuations, and use it to investigate the stability of the topological phase by calculating the topological entropy.