Asymptotic correlation functions and FFLO signature for the one-dimensional attractive Hubbard model

TL;DR

This paper analyzes the asymptotic behavior of correlation functions in the 1D attractive Hubbard model, revealing oscillating patterns and momentum peaks indicative of an FFLO-like state, using Bethe ansatz and conformal field theory.

Contribution

It provides the first detailed analytical characterization of FFLO signatures in the 1D Hubbard model's correlation functions.

Findings

Correlation functions exhibit oscillations with power-law decay.

Momentum space peaks at the Fermi surface mismatch $ riangle k_F$.

Evidence of FFLO-like pairing in the 1D Hubbard model.

Abstract

We study the long-distance asymptotic behavior of various correlation functions for the one-dimensional (1D) attractive Hubbard model in a partially polarized phase through the Bethe ansatz and conformal field theory approaches. We particularly find the oscillating behavior of these correlation functions with spatial power-law decay, of which the pair (spin) correlation function oscillates with a frequency $\Delta k_F$ ($2\Delta k_F$). Here $\Delta k_F=\pi(n_\uparrow-n_\downarrow)$ is the mismatch in the Fermi surfaces of spin-up and spin-down particles. Consequently, the pair correlation function in momentum space has peaks at the mismatch $k=\Delta k_F$, which has been observed in recent numerical work on this model. These singular peaks in momentum space together with the spatial oscillation suggest an analog of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in the 1D Hubbard model. The parameter $\beta$ representing the lattice effect becomes prominent in critical exponents which determine the power-law decay of all correlation functions. We point out that the backscattering of unpaired fermions and bound pairs within their own Fermi points gives a microscopic origin of the FFLO pairing in 1D.