Interaction and thermodynamics of spinons in the XX chain

Details Interaction and thermodynamics of spinons in the XX chain Interaction and thermodynamics of spinons in the XX chain

2007-10-16

arxiv.org/abs/0710.3097v1

Physics

Condensed Matter

Strongly Correlated Electrons

16 pages, 3 figures

Scientific paper

10.1088/1751-8113/41/20/205002

The mapping between the fermion and spinon compositions of eigenstates in the one-dimensional spin-1/2 XX model on a lattice with N sites is used to describe the spinon interaction from two different perspectives: (i) For finite N the energy of all eigenstates is expressed as a function of spinon momenta and spinon spins, which, in turn, are solutions of a set of Bethe ansatz equations. The latter are the basis of an exact thermodynamic analysis in the spinon representation of the XX model. (ii) For N -> infinity the energy per site of spinon configurations involving any number of spinon orbitals is expressed as a function of reduced variables representing momentum, filling, and magnetization of each orbital. The spins of spinons in a single orbital are found to be coupled in a manner well described by an Ising-like equivalent-neighbor interaction, switching from ferromagnetic to antiferromagnetic as the filling exceeds a critical level. Comparisons are made with results for the Haldane-Shastry model.

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