XXZ Bethe states as highest weight vectors of the $sl_2$ loop algebra at roots of unity
| dc.creator | Deguchi, Tetsuo | |
| dc.date | 2005-03-23 | |
| dc.date | 2007-07-03 | |
| dc.date.accessioned | 2026-07-07T08:13:36Z | |
| dc.date.available | 2026-07-07T08:13:36Z | |
| dc.description | We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at roots of unity is a highest weight vector of the $sl_2$ loop algebra, for some restricted sectors with respect to eigenvalues of the total spin operator $S^Z$, and evaluate explicitly the highest weight in terms of the Bethe roots. We also discuss whether a given regular Bethe state in the sectors generates an irreducible representation or not. In fact, we present such a regular Bethe state in the inhomogeneous case that generates a reducible Weyl module. Here, we call a solution of the Bethe ansatz equations which is given by a set of distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}. | |
| dc.description | 40pages; revised version | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0503564 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0503564 | |
| dc.identifier | J. Phys. A: Math. Theor. Vol. 40 (2007) pp. 7473-7508 | |
| dc.identifier | doi:10.1088/1751-8113/40/27/005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132823 | |
| dc.subject | Statistical Mechanics | |
| dc.title | XXZ Bethe states as highest weight vectors of the $sl_2$ loop algebra at roots of unity | |
| dc.type | text |