We perform a comparative study of the finite temperature behavior of ultracold Bose atoms in optical lattices by the slave fermion and the slave boson approaches to the Bose-Hubbard model. The phase diagram of the system is presented. Although both approaches are equivalent without approximations, the mean field theory based on the slave fermion technique is quantitatively more appropriate. Conceptually, the slave fermion approach automatically excludes the double occupancy of two identical fermions on the same lattice site. By comparing to known results in limiting cases, we find the slave fermion approach better than the slave boson approach. For example, in the non-interacting limit, the critical temperature of the superfluid-normal liquid transition calculated by the slave fermion approach is closer to the well-known ideal Bose gas result. At zero-temperature limit of the critical interaction, strength from the slave fermion approach is also closer to that from the direct calculation using a zero-temperature mean field theory.
We discuss the emergence of
p-wave superfluidity of identical atomic fermions in a two-dimensional optical lattice. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices the scattering amplitude is strongly reduced compared to free space due to a small overlap of wave functions of fermions sitting in the neighboring lattice sites, which suppresses the
p-wave superfluidity. However, for moderate lattice depths the enhancement of the density of states can compensate the decrease of the scattering amplitude. Moreover, the lattice setup significantly reduces inelastic collisional losses, which allows one to get closer to a
p-wave Feshbach resonance. This opens possibilities to obtain the topological
px+ipy superfluid phase, especially in the recently proposed subwavelength lattices. We demonstrate this for the two-dimensional version of the Kronig-Penney model allowing a transparent physical analysis.
In this work we discuss the extraction of mean field single particle Hamiltonians from a many body wave function of a fermionic system. While we primarily discuss lattice models we also look at neon in an augccpvdz basis set as an example. Our approach allows us to discuss the result of a many particle wave function in terms of a non-interacting description. In contrast to density functional theory approaches on the lattice this approach allows the extraction of appropriate kinetic terms. In result the extracted mean field theories are closer to the physics of the problem under investigation. Therefore, the extracted mean field Hamiltonians may provide an improved starting point for perturbative approaches. In addition, the technique can be used to decide whether a density matrix renormalization group calculation for interacting fermions has converged to the true ground state.