Analytical thermodynamics of a strongly attractive three-component Fermi gas in one dimension

TL;DR

This paper analytically studies the thermodynamics and phase transitions of a strongly attractive three-component one-dimensional Fermi gas with SU(3) symmetry, revealing rich quantum phases and critical behaviors.

Contribution

It derives the analytical thermodynamics of the system using the thermodynamic Bethe ansatz, including phase diagrams and crossover behaviors between different Tomonaga-Luttinger liquids.

Findings

System behaves as two- or three-component Tomonaga-Luttinger liquid at low temperature.

Phase diagrams for chemical potential and specific heat are provided.

Crossover between phases shows singular behavior in thermodynamic quantities.

Abstract

Ultracold three-component atomic Fermi gases in one dimension are expected to exhibit rich physics due to the presence of trions and different pairing states. Quantum phase transitions from the trion state into a paired phase and a normal Fermi liquid occur at zero temperature. We derive the analytical thermodynamics of strongly attractive three-component one-dimensional fermions with SU(3) symmetry via the thermodynamic Bethe ansatz method in unequal Zeeman splitting fields $H_1$ and $H_2$. We find explicitly that for low temperature the system acts like either a two-component or a three-component Tomonaga-Luttinger liquid dependent on the system parameters. The phase diagrams for the chemical potential and specific heat are presented for illustrative values of the Zeeman splitting. We also demonstrate that crossover between different Tomonaga-Luttinger liquid phases evolve singular behaviour in specific heat and entropy as the temperature tends to zero. Beyond Tomonaga-Luttinger liquid physics, we obtain the equation of state which provides a precise description of universal thermodynamics and quantum criticality in three-component strongly attractive Fermi gases.