Universal properties of Fermi gases in one dimension

Abstract

In this Rapid Communication, we investigate the universal properties of a spin-polarized two-component Fermi gas in one dimension (1D) using the Bethe ansatz. We discuss the quantum phases and phase transitions by obtaining exact results for the equation of state, the contact, the magnetic susceptibility, and the contact susceptibility, giving a precise understanding of the 1D analog of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in three dimensions (3D) and the associated universal magnetic properties. In particular, we obtain the exact form of the magnetic susceptibility χ∼1/T√exp(−Δ/T) at low temperatures, where Δ is the energy gap and T is the temperature. Moreover, we establish exact upper and lower bounds for the relation between polarization P and the contact C for both repulsive and attractive Fermi gases. Our findings emphasize the role of pair fluctuations in strongly interacting 1D fermion systems that can shed light on higher dimensions. Show more