Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus

TL;DR

This paper analyzes the entanglement spectra of non-Abelian Moore-Read fractional quantum Hall states on a torus, revealing complex sector combinations and edge physics insights, with implications for other topological systems.

Contribution

It provides a microscopic understanding of entanglement spectra and edge structures in Moore-Read states on the torus, connecting conformal field theory sectors to entanglement features.

Findings

Entanglement spectra decompose into sector combinations.

Edge level counting aligns with conformal field theory predictions.

Boundary entropy density exceeds that of Laughlin states.

Abstract

We present a detailed analysis of bi-partite entanglement in the non-Abelian Moore-Read fractional quantum Hall state of bosons and fermions on the torus. In particular, we show that the entanglement spectra can be decomposed into intricate combinations of different sectors of the conformal field theory describing the edge physics, and that the edge level counting and tower structure can be microscopically understood by considering the vicinity of the thin-torus limit. We also find that the boundary entropy density of the Moore-Read state is markedly higher than in the Laughlin states investigated so far. Despite the torus geometry being somewhat more involved than in the sphere geometry, our analysis and insights may prove useful when adopting entanglement probes to other systems that are more easily studied with periodic boundary conditions, such as fractional Chern insulators and lattice problems in general.