Continuum limit of lattice models with Laughlin-like ground states containing quasiholes

Abstract

There has been a significant interest in the last years in finding fractional quantum Hall physics in lattice models, but it is not always clear how these models connect to the corresponding models in continuum systems. Here we introduce a family of models that is able to interpolate between a recently proposed set of lattice models with Laughlin-like ground states constructed from conformal field theory and models with ground states that are practically the usual bosonic/fermionic Laughlin states in the continuum. Both the ground state and the Hamiltonian are known analytically, and we find that the Hamiltonian in the continuum limit does not coincide with the usual delta interaction Hamiltonian for the Laughlin states. We introduce quasiholes into the models and show analytically that their braiding properties are as expected if the quasiholes are screened. We demonstrate screening numerically for the 1/3 Laughlin model and find that the quasiholes are slightly smaller in the continuum than in the lattice. Finally, we compute the effective magnetic field felt by the quasiholes and show that it is close to uniform when approaching the continuum limit. The techniques presented here to interpolate between the lattice and the continuum can also be applied to other fractional quantum Hall states that are constructed from conformal field theory.

8 pages, 7 figures; v2: minor changes and accepted for publication in Phys. Rev. B

References in corpus (6)

• Fractional Quantum Hall Effect in Optical Lattices
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Characterization of quasiholes in fractional Chern insulators

Cited by in corpus (12)

• Recent Developments in Fractional Chern Insulators
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Real-space probe for lattice quasiholes
• Lattice Laughlin states on the torus from conformal field theory
• Laughlin topology on fractal lattices without area law entanglement
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Continuum limit of lattice quasielectron wavefunctions
• Structure of the nearly-degenerate manifold of lattice quasiholes on a torus
• Dyadic Greens function for a topological insulator stratified sphere
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids