Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases

TL;DR

This paper investigates how local interactions along an entanglement cut in 2+1D Abelian topological phases influence the entanglement spectrum and entropy, revealing sensitivity to boundary conditions and effects on topological entanglement entropy.

Contribution

It provides a detailed analysis of how multiple edge phases and local tunneling interactions affect entanglement properties in topological phases.

Findings

Entanglement spectrum depends on local tunneling interactions.

Local interactions can increase the topological entanglement entropy.

Tunneling interactions act as barriers to quasiparticle transport.

Abstract

A given fractional quantum Hall state may admit multiple, distinct edge phases on its boundary. We explore the implications that multiple edge phases have for the entanglement spectrum and entropy of a given bulk state. We describe the precise manner in which the entanglement spectrum depends upon local (tunneling) interactions along an entanglement cut and throughout the bulk. The sensitivity to local conditions near the entanglement cut appears not only in gross features of the spectrum, but can also manifest itself in an additive, positive constant correction to the topological entanglement entropy, i.e., it increases its magnitude. A natural interpretation for this result is that the tunneling interactions across an entanglement cut can function as a barrier to certain types of quasiparticle transport across the cut, thereby, lowering the total entanglement between the two regions.