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Free fermion branches in some quantum spin models

F. C. Alcaraz·Yu. G. Stroganov
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Abstract

Extensive numerical analysis of the eigenspectra of the $SU_q(N)$ invariant Perk-Schultz Hamiltonian shows some simple regularities for a significant part of the eigenspectrum. Inspired by those results we have found two set of solutions of the associated nested Bethe-ansatz equations. The first set is obtained at a special value of the anisotropy ($q = \exp(i2π(N-1)/N)$) and describes in particular the ground state and nearby excitations as a sum of free-fermion quasienergies. The second set of solutions provides the energies in the sectors whose number $n_i$ of particles of distinct species ($i =0, >..., N-1$) are less or equal to the unity except for one of the species. For this last set we obtain the eigenspectra of a free fermion model for arbitrary values of the anisotropy.

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F. C. Alcaraz, Yu. G. Stroganov. 2002-05-27. Free fermion branches in some quantum spin models. https://doi.org/10.1088/0305-4470%2F35%2F32%2F301

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