Extended Bose-Hubbard model with incompressible states at fractional numbers

TL;DR

This paper extends the Bose-Hubbard model to include long-range interactions, revealing incompressible states at fractional fillings that relate to fractional quantum Hall states, with implications for optical lattice experiments.

Contribution

It introduces an extended Bose-Hubbard model incorporating long-range interactions and demonstrates the emergence of incompressible states at fractional fillings.

Findings

Incompressible Mott insulator states at fractional fillings are identified.

These states are compatible with fractional quantum Hall filling fractions.

The stability of these states under hopping perturbations is discussed.

Abstract

The Bose-Hubbard model is extended to include nearest and far neighbor interactions and is related to the fractional quantum Hall effect (FQHE). Both models may be studied in optical lattices with quantum gases. The ground state is calculated for the extended Bose-Hubbard model with strong repulsive interactions (weak hopping). Incompressible Mott insulator states are found at rational filling fractions compatible with the principal and secondary FQHE filling fractions of the lowest Landau levels observed experimentally. It is discussed to which extent these states at fractional filling survive or undergoes a Mott insulator transition to a superfluid as hopping terms are included.