Analytic Expression for the Entanglement Entropy of a 2D Topological Superconductor

TL;DR

This paper derives an analytical expression for the entanglement entropy in a 2D topological superconductor model, revealing how it signals phase transitions through cusps and divergences related to Fermi surface changes.

Contribution

It provides the first analytical approximation of entanglement entropy in a 2D topological superconductor, linking Fermi surface topology to entanglement behavior at phase transitions.

Findings

Entanglement entropy exhibits cusps at topological phase transitions.

The analytical expression captures the divergence of entropy derivative near transitions.

Fermi surface count determines the topological invariant and entanglement features.

Abstract

We study a model of two dimensional, topological superconductivity on a square lattice. The model contains hopping, spin orbit coupling and a time reversal symmetry breaking Zeeman term. This term, together with the chemical potential act as knobs that induce transitions between trivial and topological superconductivity. As previously found numerically, the transitions are seen in the entanglement entropy as cusps as a function of model parameters. In this work we study the entanglement entropy analytically by keeping only its most important components. Our study is based on the intuition that the number of Fermi surfaces in the system controls the topological invariant. With our approximate expression for the entanglement entropy we are able to extract the divergent entanglement entropy derivative close to the phase transition.