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

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

2010-10-31

arxiv.org/abs/1011.0128v2

J. Phys. A: Math. Theor. 44 (2011) 165002

Physics

Condensed Matter

Quantum Gases

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

Scientific paper

10.1088/1751-8113/44/16/165002

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.

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