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

TL;DR

This paper introduces a family of models that smoothly connect lattice fractional quantum Hall states with their continuum counterparts, analyzing their ground states, quasiholes, and effective magnetic fields.

Contribution

It provides an analytical interpolation between lattice and continuum Laughlin states, revealing differences in Hamiltonians and quasihole properties.

Findings

Hamiltonian in the continuum limit differs from delta interaction model.

Quasiholes are screened and slightly smaller in the continuum.

Effective magnetic field becomes more uniform approaching the continuum.

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.