FFLO correlation and free fluids in the one-dimensional attractive Hubbard model

TL;DR

This paper demonstrates that the low-energy properties of the 1D attractive Hubbard model can be described as two free fluids of bound pairs and unpaired fermions, revealing universal behaviors and simple additivity in thermodynamics.

Contribution

It analytically derives the FFLO pairing correlations and shows the effective free fluid behavior of bound pairs and unpaired fermions in the 1D attractive Hubbard model.

Findings

Low temperature phase diagram identified.

FFLO pairing correlation function analytically calculated.

Thermodynamics exhibit additivity rules indicating free particle behavior.

Abstract

In this Rapid Communication we show that low energy macroscopic properties of the one-dimensional (1D) attractive Hubbard model exhibit two fluids of bound pairs and of unpaired fermions. Using the thermodynamic Bethe ansatz equations of the model, we first determine the low temperature phase diagram and analytically calculate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing correlation function for the partially-polarized phase. We then show that for such a FFLO-like state in the low density regime the effective chemical potentials of bound pairs and unpaired fermions behave like two free fluids. Consequently, the susceptibility, compressibility and specific heat obey simple additivity rules, indicating the `free' particle nature of interacting fermions on a 1D lattice. In contrast to the continuum Fermi gases, the correlation critical exponents and thermodynamics of the attractive Hubbard model essentially depend on two lattice interacting parameters. Finally, we study scaling functions, the Wilson ratio and susceptibility which provide universal macroscopic properties/dimensionless constants of interacting fermions at low energy.