Universal Properties of Fermi Gases in One-dimension

TL;DR

This paper uses Bethe ansatz to analyze the universal properties and phase transitions of a 1D spin-polarized Fermi gas, revealing exact results for thermodynamics, magnetic susceptibility, and polarization-contact relations, highlighting pair fluctuations.

Contribution

It provides the first exact analysis of the universal properties and phase behavior of 1D Fermi gases, including precise formulas for magnetic susceptibility and bounds for polarization-contact relations.

Findings

Exact form of magnetic susceptibility at low T

Universal bounds for polarization and contact

Insights into pair fluctuations in 1D fermion systems

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.