The one-dimensional (1D) Fermi Hubbard model describing interacting fermions on a lattice provides a paradigm of many-body physics, including spin-charge separation, fractional excitations, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing, Mott insulating phase and phase transitions. Very recently, ultracold atoms trapped in optical lattices offer promising opportunities to test such traditional concepts. However, most of these studies were particularly restricted to repulsive interaction. The 1D attractive Hubbard model is a notoriously difficult problem and rarely studied in the literature due to the complicated bound states of multi-particles.
In this talk, I will present my study on the universal thermodynamics and the quantum correlations of this model. Using the thermodynamic Bethe ansatz equations, I derive the equation of state in the strong coupling regime, from which the uniform scaling functions at quantum criticality are obtained. The analytical results agree well with the numerics, and could be used in fitting experimental data. Specific to the FFLO-like state, I obtain the effective chemical potentials of two °∞non-interacting Fermi liquids°± and additivity rules of the susceptibility, compressibility and specific heat which reveal a free Fermi liquid nature; I study the long-distance asymptotics of correlation functions at zero temperature, and I find that in contrast to the continuum Fermi gases, the correlation critical exponents, thermodynamics, Luttinger parameter, and Wilson ratio of the attractive Hubbard model essentially depend on two lattice interacting parameters, all of which under the lattice-gas map can be reduced to the case of a Fermi gas.
This study provides a precise understanding of the universal low energy physics of attractive fermions on a lattice, and a benchmark for ultracold atom experiments.