An Effective Field Theory for One-dimensional Polarized Fermi Gases

Abstract

We derive an effective field theory describing the long wavelength, low energy properties of one-dimensional (1D) attractive Fermi gases with spin imbalance. Our theory is based on the exact solution (Bethe ansatz) of the microscopic Hamiltonian, the Gaudin-Yang model. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a novel quantum fluid, a two-component Luttinger liquid with spin-charge mixing. Applying the theory, we obtain the correlation functions and the universal low temperature thermodynamics. Our theory can also predict the phase diagram of weakly coupled 1D gases, a quasi-1D system recently realized in experiments at Rice university.