Quantum Phase Transitions of Ultra Cold Gases in the Fermi-Bose Hubbard Hamiltonian*

The experimental realization of ultracold fermions has stimulated work on theoretical models of zero-temperature quantum phase transitions and the BCS-BEC crossover. Ultracold gases confined in optical lattices can demonstrate a wide range of different phases by varying controllable system parameters, such as optical lattice intensity, particle number, spin composition and atomic interactions. We perform numerical studies of a Fermi-Bose-Hubbard Hamiltonian with the Vidal algorithm (Time Evolving Block Decimation). Our Hamiltonian treats a one dimensional system of fermions coupled to a bosonic molecular state, as occurs in Feshbach resonances, and encompasses a very large parameter space. We present the quantum phase diagram, focusing on small systems and the most experimentally relevant parameters.