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Physical Review Letters

Thermodynamics of Fermions in One Dimension with a δ -Function Interaction

Cheng Kee Lai

Published Jun 14, 1971• 59 citations
Publisher

Abstract

The equilibrium thermodynamics of a one-dimensional fermion system with a repulsive $\ensuremath{\delta}$-function interaction is found to be derivable from the solution of a set of coupled integral equations. The equations for the attractive case are also given.

DOI
10.1103/physrevlett.26.1472

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The equilibrium thermodynamics of a one-dimensional fermion system with a repulsive \ensuremathδ\ensuremath{\delta}\ensuremathδ-function interaction is found to be derivable from the solution of a set of coupled integral equations. The equations for the attractive case are also given.
The author considers a gas of fermions with parabolic dispersion and N spin-components (or spin S, N=2S+1) with SU(N) symmetry in one dimension interacting via a delta -function potential. The model is integrable and its solution has been obtained by Sutherland in terms of N nested Bethe ansatze. He analyses the discrete Bethe ansatz equations and classifies their solutions according to the string hypothesis. The thermodynamic Bethe-ansatz equations are derived for arbitrary band-filling for both repulsive and attractive interaction in terms of the thermodynamic energy potentials for the classes of eigenstates of the Hamiltonian. These equations are then discussed in several limiting cases, e.g. S=1/2, the ground state (T to 0), for vanishing interaction strength, for strong coupling, in the high-temperature limit, and the large-N limit.