Particle Entanglement Spectra for Quantum Hall states on Lattices

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.

12 pages, 9 figures

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Cited by in corpus (7)

• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Chiral Bosonic Phases on the Haldane Honeycomb Lattice
• Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
• Interacting bosons in topological optical flux lattices
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Two-dimensional topological order of kinetically constrained quantum particles
• Many-Body Chern Numbers of $\nu =1/3$ and $1/2$ States on Various Lattices