Quantum phase transitions in the Fermi-Bose Hubbard model

TL;DR

This paper introduces a multi-band Fermi-Bose Hubbard model to describe atomic Fermi gases in optical lattices with Feshbach resonances, analyzing quantum phase transitions and Mott-superfluid boundaries.

Contribution

It develops a new Hamiltonian model incorporating fermion-boson conversion and solves it in a two-state approximation, revealing complex phase diagram features near resonance.

Findings

Reproduces known phase transitions in large detuning limits

Identifies superposition states in Mott phases near resonance

Shows avoided crossing behavior in phase diagram

Abstract

We propose a multi-band Fermi-Bose Hubbard model with on-site fermion-boson conversion and general filling factor in three dimensions. Such a Hamiltonian models an atomic Fermi gas trapped in a lattice potential and subject to a Feshbach resonance. We solve this model in the two state approximation for paired fermions at zero temperature. The problem then maps onto a coupled Heisenberg spin model. In the limit of large positive and negative detuning, the quantum phase transitions in the Bose Hubbard and Paired-Fermi Hubbard models are correctly reproduced. Near resonance, the Mott states are given by a superposition of the paired-fermion and boson fields and the Mott-superfluid borders go through an avoided crossing in the phase diagram.