Spectrum of a spin chain with inverse square exchange

Details Spectrum of a spin chain with inverse square exchange Spectrum of a spin chain with inverse square exchange

1993-03-26

arxiv.org/abs/cond-mat/9303050v1

J. Phys. A 26 (1993) L473

Physics

Condensed Matter

9 pages, latex

Scientific paper

10.1088/0305-4470/26/10/002

The spectrum of a one-dimensional chain of $SU(n)$ spins positioned at the static equilibrium positions of the particles in a corresponding classical Calogero system with an exchange interaction inversely proportional to the square of their distance is studied. As in the translationally invariant Haldane--Shastry model the spectrum is found to exhibit a very simple structure containing highly degenerate ``super-multiplets''. The algebra underlying this structure is identified and several sets of raising and lowering operators are given explicitely. On the basis of this algebra and numerical studies we give the complete spectrum and thermodynamics of the $SU(2)$ system.

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