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 (9)

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• Universal Tomonaga-Luttinger liquid phases in one-dimensional strongly attractive SU(N) fermionic cold atoms
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Cited by in corpus (6)

• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Dimensionless ratios: characteristics of quantum liquids and their phase transitions
• Three roads to the energy gap
• A unified approach to the thermodynamics and quantum scaling functions of one-dimensional strongly attractive $SU(w)$ Fermi Gases
• Impurity immersed in a two-component few-fermion mixture in a one-dimensional harmonic trap
• Expansion of one-dimensional spinor gases from power-law traps