Asymptotic correlation functions and FFLO signature for the one-dimensional attractive spin-1/2 Fermi gas

TL;DR

This paper analyzes the asymptotic behavior of correlation functions in a one-dimensional attractive spin-1/2 Fermi gas, revealing FFLO signatures and the microscopic origin of spatial oscillations related to Fermi surface mismatches.

Contribution

It demonstrates that backscattering causes FFLO-like oscillations in correlation functions and identifies the momentum-space peak at Fermi surface mismatch as a key signature.

Findings

Correlation functions exhibit power-law decay with oscillations depending on Fermi surface mismatch.

Spatial oscillations are characteristic of a 1D FFLO state due to backscattering.

Momentum-space pair correlation peaks at the Fermi surface mismatch.

Abstract

We investigate the long distance asymptotics of various correlation functions for the one-dimensional spin-1/2 Fermi gas with attractive interactions using the dressed charge formalism. In the spin polarized phase, these correlation functions exhibit spatial oscillations with a power-law decay whereby their critical exponents are found through conformal field theory. We show that spatial oscillations of the leading terms in the pair correlation function and the spin correlation function solely depend on $\Delta k_F$ and $2\Delta k_F$, respectively. Here $\Delta k_F=\pi(n_{\uparrow}-n_{\downarrow})$ denotes the mismatch between the Fermi surfaces of spin-up and spin-down fermions. Such spatial modulations are characteristics of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Our key observation is that backscattering among the Fermi points of bound pairs and unpaired fermions results in a one-dimensional analog of the FFLO state and displays a microscopic origin of the FFLO nature. Furthermore, we show that the pair correlation function in momentum space has a peak at the point of mismatch between both Fermi surfaces $k=\Delta k_F$, which has recently been observed in numerous numerical studies.