The open XXZ spin chain in the SoV framework: scalar product of separate states
| Autor: | Nikolai Kitanine, Véronique Terras, J. M. Maillet, Giuliano Niccoli |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bourgogne [Dijon] (IMB), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL) |
| Rok vydání: | 2018 |
| Předmět: |
High Energy Physics - Theory
Statistics and Probability Integrable system Diagonal form [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] Scalar (mathematics) FOS: Physical sciences General Physics and Astronomy algebra determinant integrability 01 natural sciences 0103 physical sciences thermodynamical correlation function Gauge theory Algebraic number 010306 general physics Condensed Matter - Statistical Mechanics Mathematical Physics Eigenvalues and eigenvectors Mathematical physics Mathematics form factor Statistical Mechanics (cond-mat.stat-mech) Nonlinear Sciences - Exactly Solvable and Integrable Systems K-matrix 010308 nuclear & particles physics Mathematical analysis Statistical and Nonlinear Physics Mathematical Physics (math-ph) Vandermonde matrix boundary condition [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] Automatic Keywords Heisenberg High Energy Physics - Theory (hep-th) Modeling and Simulation Thermodynamic limit Exactly Solvable and Integrable Systems (nlin.SI) transformation: gauge spin: chain |
| Zdroj: | J.Phys.A J.Phys.A, 2018, 51 (48), pp.485201. ⟨10.1088/1751-8121/aae76f⟩ |
| ISSN: | 1751-8121 1751-8113 |
| DOI: | 10.1088/1751-8121/aae76f |
| Popis: | In our previous paper [1] we have obtained, for the XXX spin-1/2 Heisenberg open chain, new determinant representations for the scalar products of separate states in the quantum separation of variables (SoV) framework. In this article we perform a similar study in a more complicated case: the XXZ open spin-1/2 chain with the most general integrable boundary terms. To solve this model by means of SoV we use an algebraic Vertex-IRF gauge transformation reducing one of the boundary K-matrices to a diagonal form. As usual within the SoV approach, the scalar products of separate states are computed in terms of dressed Vandermonde determinants having an intricate dependency on the inhomogeneity parameters. We show that these determinants can be transformed into different ones in which the homogeneous limit can be taken straightforwardly. These representations generalize in a non-trivial manner to the trigonometric case the expressions found previously in the rational case. We also show that generically all scalar products can be expressed in a form which is similar to - although more cumbersome than - the well-known Slavnov determinant representation for the scalar products of the Bethe states of the periodic chain. Considering a special choice of the boundary parameters relevant in the thermodynamic limit to describe the half infinite chain with a general boundary, we particularize these representations to the case of one of the two states being an eigenstate. We obtain simplified formulas that should be of direct use to compute the form factors and correlation functions of this model. 55 pages |
| Databáze: | OpenAIRE |
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