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 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 analogue of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in three dimension (3D) and the associated universal magnetic properties. In particular, we obtain the exact form of the magnetic susceptibility $\chi \sim 1/\sqrt{T}\exp (-\Delta /T)$ at low temperatures, where $\Delta$ 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 the pair fluctuations in strongly interacting 1D fermion systems that can shed light on higher dimensions.

4 figures, the main paper

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• Finite temperature contact for SU(2) fermions trapped in a 1D harmonic confinement
• Complex Langevin study for polarons in an attractively interacting one-dimensional two-component Fermi gas
• Low-Dimensional Fluctuations and Pseudogap in Gaudin-Yang Fermi Gases
• Spin correlations and entanglement in partially magnetised ensembles of fermions
• Universal principles for sudden-quench quantum Otto engines