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arXiv:cond-mat/0011270 · Physical review. B, Condensed matter

Coordinate representation of the two-spinon wave function and spinon interaction in the Haldane-Shastry model

Bogdan Andrei Bernevig, Domenico Giuliano, R. B. Laughlin

Published Jun 22, 2001• 25 citations
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Abstract

By deriving and studying the coordinate representation for the two-spinon wave function, we show that spinon excitations in the Haldane-Shastry model interact. The interaction is given by a short-range attraction and causes an enhancement in the two-spinon wave function at short separations between the spinons. We express the spin susceptibility for a finite lattice in terms of the enhancement, given by the two-spinon wave function at zero separation. In the thermodynamic limit, the spinon attraction turns into the square-root divergence in the dynamical spin susceptibility.

DOI
10.1103/physrevb.64.024425

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By deriving and studying the coordinate representation for the two-spinon wave function, we show that spinon excitations in the Haldane-Shastry model interact. The interaction is given by a short-range attraction and causes an enhancement in the two-spinon wave function at short separations between the spinons. We express the spin susceptibility for a finite lattice in terms of the enhancement, given by the two-spinon wave function at zero separation. In the thermodynamic limit, the spinon attraction turns into the square-root divergence in the dynamical spin susceptibility.
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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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