Numerically exact simulations of strongly interacting fermions in an optical lattice

We present large scale variational matrix product state (MPS) simulations of the Fermi-Bose Hubbard model, which is an effective two-channel resonance model for a strongly interacting two-component Fermi gas in an optical lattice. The Hubbard parameters appearing in this model are determined from the exact solution of the two-fermion problem including interband couplings and renormalization of the molecular energy in the closed channel.\footnote{H. P. B\"uchler, {\it Phys. Rev. Lett.} {\bf 104} 090402 (2010)} This approach allows us to quantitatively determine the phase diagram of alkali atoms interacting via a Feshbach resonance in a quasi-1D geometry as a function of the experimental parameters. The applicability of this model to describe dynamics across a Feshbach resonance will also be discussed.