The Wave Functions for the Free-Fermion Part of the Spectrum of the $SU_q(N)$ Quantum Spin Models

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dc.creatorAlcaraz, F. C.
dc.creatorStroganov, Yu. G.
dc.date2002-12-19
dc.date.accessioned2026-07-07T10:43:59Z
dc.date.available2026-07-07T10:43:59Z
dc.descriptionWe conjecture that the free-fermion part of the eigenspectrum observed recently for the $SU_q(N)$ Perk-Schultz spin chain Hamiltonian in a finite lattice with $q=\exp (iπ(N-1)/N)$ is a consequence of the existence of a special simple eigenvalue for the transfer matrix of the auxiliary inhomogeneous $SU_q(N-1)$ vertex model which appears in the nested Bethe ansatz approach. We prove that this conjecture is valid for the case of the SU(3) spin chain with periodic boundary condition. In this case we obtain a formula for the components of the eigenvector of the auxiliary inhomogeneous 6-vertex model ($q=\exp (2 i π/3)$), which permit us to find one by one all components of this eigenvector and consequently to find the eigenvectors of the free-fermion part of the eigenspectrum of the SU(3) spin chain. Similarly as in the known case of the $SU_q(2)$ case at $q=\exp(i2π/3)$ our numerical and analytical studies induce some conjectures for special rates of correlation functions.
dc.description25 pages and no figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0212475
dc.identifierhttp://arxiv.org/abs/cond-mat/0212475
dc.identifierJ.Phys.A36:2381-2397,2003
dc.identifierdoi:10.1088/0305-4470/36/10/301
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/182438
dc.subjectStatistical Mechanics
dc.subjectStrongly Correlated Electrons
dc.subjectHigh Energy Physics - Theory
dc.titleThe Wave Functions for the Free-Fermion Part of the Spectrum of the $SU_q(N)$ Quantum Spin Models
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