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

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.

22 pages, 2 figures, slight improvements, some extra references

References in corpus (5)

• Phase diagram of a strongly interacting polarized Fermi gas in one dimension
• Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases
• Exact quantum Monte Carlo study of one dimensional trapped fermions with attractive contact interactions
• Magnetic Phase Transitions in One-dimensional Strongly Attractive Three-Component Ultracold Fermions
• Unified description of pairing, trionic and quarteting states for one-dimensional SU(4) attractive fermions