Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases

Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases

The modified algebraic Bethe ansatz, introduced by Crampé and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-12 chain on the segment with lower and upper triangular boundaries. The eigenvalues and the eigenvectors are conjectured. They are characterized by a...

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Main Author: Samuel Belliard
Format: Article
Language:English
Published: Elsevier 2015-03-01
Series:Nuclear Physics B
Online Access:http://www.sciencedirect.com/science/article/pii/S0550321315000061
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spelling doaj-1fce831d14d6477da924399abf5fea262020-11-24T23:50:08ZengElsevierNuclear Physics B0550-32132015-03-01892120Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular casesSamuel Belliard0Laboratoire de Physique Théorique et Modélisation (CNRS UMR 8089), Université de Cergy-Pontoise, F-95302 Cergy-Pontoise, FranceThe modified algebraic Bethe ansatz, introduced by Crampé and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-12 chain on the segment with lower and upper triangular boundaries. The eigenvalues and the eigenvectors are conjectured. They are characterized by a set of Bethe roots with cardinality equal to N the length of the chain and which satisfies a set of Bethe equations with an additional term. The conjecture follows from exact results for small chains. We also present a factorized formula for the Bethe vectors of the Heisenberg XXZ spin-12 chain on the segment with two upper triangular boundaries.http://www.sciencedirect.com/science/article/pii/S0550321315000061
collection DOAJ
language English
format Article
sources DOAJ
author Samuel Belliard
spellingShingle Samuel Belliard
Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases
Nuclear Physics B
author_facet Samuel Belliard
author_sort Samuel Belliard
title Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases
title_short Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases
title_full Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases
title_fullStr Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases
title_full_unstemmed Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases
title_sort modified algebraic bethe ansatz for xxz chain on the segment – i: triangular cases
publisher Elsevier
series Nuclear Physics B
issn 0550-3213
publishDate 2015-03-01
description The modified algebraic Bethe ansatz, introduced by Crampé and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-12 chain on the segment with lower and upper triangular boundaries. The eigenvalues and the eigenvectors are conjectured. They are characterized by a set of Bethe roots with cardinality equal to N the length of the chain and which satisfies a set of Bethe equations with an additional term. The conjecture follows from exact results for small chains. We also present a factorized formula for the Bethe vectors of the Heisenberg XXZ spin-12 chain on the segment with two upper triangular boundaries.
url http://www.sciencedirect.com/science/article/pii/S0550321315000061
work_keys_str_mv AT samuelbelliard modifiedalgebraicbetheansatzforxxzchainonthesegmentitriangularcases
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