Particle Entanglement Spectra for Quantum Hall states on Lattices

TL;DR

This paper uses particle entanglement spectra to analyze bosonic quantum Hall states on lattices, comparing trial wavefunctions and groundstates to understand topological order and phase competition.

Contribution

It provides a comparative analysis of entanglement spectra for known trial states and lattice groundstates, revealing insights into topological order and phase transitions.

Findings

Entanglement gap varies with interaction strength, indicating Landau-level mixing.

Entanglement spectra can detect competing phases like Bose-Einstein condensates.

Performance of entanglement gap and overlaps as topological indicators is evaluated.

Abstract

We use particle entanglement spectra to characterize bosonic quantum Hall states on lattices, motivated by recent studies of bosonic atoms on optical lattices. Unlike for the related problem of fractional Chern insulators, very good trial wavefunctions are known for fractional quantum Hall states on lattices. We focus on the entanglement spectra for the Laughlin state at $\nu=1/2$ for the non-Abelian Moore-Read state at $\nu=1$. We undertake a comparative study of these trial states to the corresponding groundstates of repulsive two-body or three-body contact interactions on the lattice. The magnitude of the entanglement gap is studied as a function of the interaction strength on the lattice, giving insights into the nature of Landau-level mixing. In addition, we compare the performance of the entanglement gap and overlaps with trial wavefunctions as possible indicators for the topological order in the system. We discuss how the entanglement spectra allow to detect competing phases such as a Bose-Einstein condensate.