Quantum phase transition in a shallow one-dimensional optical lattice

TL;DR

This paper investigates the quantum phase transition in a shallow one-dimensional optical lattice using the extended Bose-Hubbard model, revealing how tunneling to distant sites influences the critical point and phase diagram shape.

Contribution

It introduces and analyzes the extended Bose-Hubbard model for shallow optical lattices, highlighting the impact of long-range tunneling on phase transition properties.

Findings

Critical tunneling value is significantly affected by distant site tunneling.

Shape of the insulating lobe in the phase diagram changes with model parameters.

Results are relevant for future quantum quench experiments.

Abstract

In this article the extended Bose-Hubbard model describing ultra-cold atoms confined in a shallow, one-dimensional optical lattice is introduced and studied by the exact diagonalization approach. All parameters of the model are related to the only relevant parameter controlled experimentally -- the depth of the optical potential. Changes in a shape of the insulating lobe in the phase diagram of the system are explored and the value of the critical tunneling for which the system undergoes the phase transition (from the insulating to the superfluid phase) is predicted. It is shown that the value of critical tunneling is substantially affected by the presence of the tunnelings to distant sites of the optical lattice. The results may have some importance in upcoming experiments on quantum quench through phase transition points.