Fractional quantum Hall states in lattices: Local models and physical implementation

TL;DR

This paper introduces a new local lattice Hamiltonian model that exhibits fractional quantum Hall-like states, derived from a Fermi-Hubbard model with topological bands, and discusses its potential realization in optical lattices.

Contribution

It presents a novel local Hamiltonian model with FQH-like ground states and shows how it can be realized from a topological Fermi-Hubbard model in optical lattices.

Findings

Constructed a spin 1/2 model with a bosonic Laughlin-like ground state.

Demonstrated the emergence of this model from a Fermi-Hubbard system with topological bands.

Proposed feasible implementation in current optical lattice experiments.

Abstract

The fractional quantum Hall (FQH) effect is one of the most striking phenomena in condensed matter physics. It is described by a simple Laughlin wavefunction and has been thoroughly studied both theoretically and experimentally. In lattice systems, however, such an effect has not been observed, there are few simple models displaying it, and only few mechanisms leading to it are known. Here we propose a new way of constructing lattice Hamiltonians with local interactions and FQH like ground states. In particular, we obtain a spin 1/2 model with a bosonic Laughlin like ground state, displaying a variety of topological features. We also demonstrate how such a model naturally emerges out of a Fermi-Hubbard like model at half filling, in which the kinetic energy part possesses bands with nonzero Chern number, and we show how this model can be implemented in an optical lattice setup with present technology.