Quantum Criticality of 1D Attractive Fermi Gas

TL;DR

This paper derives an analytical equation of state for a 1D strongly attractive Fermi gas, revealing universal quantum critical scaling behaviors and providing methods to identify phase boundaries experimentally.

Contribution

It presents a comprehensive analytical framework for understanding quantum criticality in 1D attractive Fermi gases, including universal scaling functions and experimental detection strategies.

Findings

Universal scaling functions for thermodynamics in quantum critical regimes

Critical properties match those of free fermions and fermion mixtures

Method to determine phase boundaries from density profiles

Abstract

We obtain an analytical equation of state for one-dimensional strongly attractive Fermi gas for all parameter regime in current experiments. From the equation of state we derive universal scaling functions that control whole thermodynamical properties in quantum critical regimes and illustrate physical origin of quantum criticality. It turns out that the critical properties of the system are described by these of free fermions and those of mixtures of fermions with mass $m$ and $2m$. We also show how these critical properties of bulk systems can be revealed from the density profile of trapped Fermi gas at finite temperatures and can be used to determine the T=0 phase boundaries without any arbitrariness.