| Texto completo | |
| Autor(es): |
Nepomechie, Rafael I.
;
Pimenta, Rodrigo A.
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Nuclear Physics B; v. 910, p. 910-928, SEP 2016. |
| Citações Web of Science: | 4 |
| Resumo | |
We consider the Temperley-Lieb (TL) open quantum spin chain with ``free{''} boundary conditions associated with the spin-s representation of quantum-deformed sl(2). We construct the transfer matrix, and determine its eigenvalues and the corresponding Bethe equations using analytical Bethe ansatz. We show that the transfer matrix has quantum group symmetry, and we propose explicit formulas for the number of solutions of the Bethe equations and the degeneracies of the transfer-matrix eigenvalues. We propose an algebraic Bethe ansatz construction of the off-shell Bethe states, and we conjecture that the on-shell Bethe states are highest-weight states of the quantum group. We also propose a determinant formula for the scalar product between an off-shell Bethe state and its on-shell dual, as well as for the square of the norm. We find that all of these results, except for the degeneracies and a constant factor in the scalar product, are universal in the sense that they do not depend on the value of the spin. In an appendix, we briefly consider the closed TL spin chain with periodic boundary conditions, and show how a previously-proposed solution can be improved so as to obtain the complete (albeit non-universal) spectrum. (C) 2016 The Authors. Published by Elsevier B.V. (AU) | |
| Processo FAPESP: | 14/20364-0 - Solução exata de modelos de vértices com fronteiras abertas |
| Beneficiário: | Rodrigo Alves Pimenta |
| Modalidade de apoio: | Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado |
| Processo FAPESP: | 16/50023-5 - Temperley-Lieb spin chains |
| Beneficiário: | Antonio Lima Santos |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 14/00453-8 - Integrabilidade em fronteiras abertas: teoria e aplicações |
| Beneficiário: | Rodrigo Alves Pimenta |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |