Exact Study of the 1D Boson Hubbard Model with a Superlattice Potential

TL;DR

This paper investigates the phase diagram of the 1D Bose-Hubbard model with a superlattice potential using quantum Monte Carlo and exact diagonalization, revealing complex phase transitions relevant to ultracold atom experiments.

Contribution

It provides a comprehensive analysis of the phase diagram including superfluid, Mott insulator, and charge density wave phases with new insights into fractional occupation insulators.

Findings

Fractional occupation insulators extend into the soft-core region.

Phase transition between Mott insulator and charge density wave insulator.

Presence of an intermediate superfluid phase at certain fillings.

Abstract

We use Quantum Monte Carlo simulations and exact diagonalization to explore the phase diagram of the Bose-Hubbard model with an additional superlattice potential. We first analyze the properties of superfluid and insulating phases present in the hard-core limit where an exact analytic treatment is possible via the Jordan-Wigner transformation. The extension to finite on-site interaction is achieved by means of quantum Monte Carlo simulations. We determine insulator/superfluid phase diagrams as functions of the on-site repulsive interaction, superlattice potential strength, and filling, finding that insulators with fractional occupation numbers, which are present in the hard-core case, extend deep into the soft-core region. Furthermore, at integer fillings, we find that the competition between the on-site repulsion and the superlattice potential can produce a phase transition between a Mott insulator and a charge density wave insulator, with an intermediate superfluid phase. Our results are relevant to the behavior of ultracold atoms in optical superlattices which are beginning to be studied experimentally.