Yang-Yang method for the thermodynamics of one-dimensional multi-component interacting fermions

TL;DR

This paper derives the thermodynamic Bethe ansatz equations for one-dimensional multi-component fermions with $SU(kappa)$ symmetry, analyzing phase diagrams and ground state energies in both attractive and repulsive regimes.

Contribution

It provides a comprehensive derivation of the thermodynamic Bethe ansatz equations for $SU(kappa)$ fermionic systems, including root patterns and phase relationships.

Findings

Derived TBA equations for $SU(kappa)$ fermions in 1D.

Analyzed phase diagrams under magnetic fields.

Quantified ground state energies in different regimes.

Abstract

Using Yang and Yang's particle-hole description, we present a thorough derivation of the thermodynamic Bethe ansatz equations for a general $SU(\kappa)$ fermionic system in one-dimension for both the repulsive and attractive regimes under the presence of an external magnetic field. These equations are derived from Sutherland's Bethe ansatz equations by using the spin-string hypothesis. The Bethe ansatz root patterns for the attractive case are discussed in detail. The relationship between the various phases of the magnetic phase diagrams and the external magnetic fields is given for the attractive case. We also give a quantitative description of the ground state energies for both strongly repulsive and strongly attractive regimes.