Finite Size Scaling of Topological Entanglement Entropy

TL;DR

This paper investigates how the topological entanglement entropy scales near a quantum phase transition in one dimension, revealing universal functions and sub-leading terms dependent on system size and topological index.

Contribution

It introduces a universal scaling form for the topological entanglement entropy's sub-leading term across a topological phase transition in one dimension.

Findings

The sub-leading term scales as L^{-1/α} with subsystem size L.

The scaling function h_α(L/ξ) is sensitive to the topological index.

The results connect entanglement entropy scaling to topological properties.

Abstract

We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a sub-leading term, which scales as $L^{-1/\alpha}$ with the size of the subsystem $L$, here $\alpha$ is the R\'{e}nyi index. This term reveals the universal scaling function $h_\alpha(L/\xi)$, where $\xi$ is the correlation length, which is sensitive to the topological index.