Аннотация:
We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.
Образец цитирования:
Samuel Belliard, Nicolas Crampé, “Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz”, SIGMA, 9 (2013), 072, 12 pp.
\RBibitem{BelCra13}
\by Samuel~Belliard, Nicolas~Cramp\'e
\paper Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
\jour SIGMA
\yr 2013
\vol 9
\papernumber 072
\totalpages 12
\mathnet{http://mi.mathnet.ru/sigma855}
\crossref{https://doi.org/10.3842/SIGMA.2013.072}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3141540}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000327734600001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84888153521}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma855
https://www.mathnet.ru/rus/sigma/v9/p72
Эта публикация цитируется в следующих 87 статьяx:
Pascal Baseilhac, Rodrigo A Pimenta, “The q-Racah polynomials from scalar products of Bethe states II”, J. Phys. A: Math. Theor., 58:12 (2025), 125205
Giuliano Niccoli, Véronique Terras, “On correlation functions for the open XXZ chain with non-longitudinal boundary fields: The case with a constraint”, SciPost Phys., 16:4 (2024)
Dmitry Chernyak, Azat M. Gainutdinov, Jesper Lykke Jacobsen, Hubert Saleur, “Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via Uqsl2 Symmetry”, SIGMA, 19 (2023), 046, 47 pp.
He-Ran Wang, Bo Li, Fei Song, Zhong Wang, “Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain”, SciPost Phys., 15:5 (2023)
Pierre-Antoine Bernard, Gauvain Carcone, Nicolas Crampé, Luc Vinet, “Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz”, SciPost Phys. Proc., 2023, no. 14
Pei H., Terras V., “On Scalar Products and Form Factors By Separation of Variables: the Antiperiodic Xxz Model”, J. Phys. A-Math. Theor., 55:1 (2022), 015205
Zheng Zh., Sun P., Xu X., Yang T., Cao J., Yang W.-L., “Thermodynamic Limit and Boundary Energy of the Spin-1 Heisenberg Chain With Non-Diagonal Boundary Fields”, SciPost Phys., 12:2 (2022), 071
Alexandre Faribault, Claude Dimo, “'Bethe-ansatz-free' eigenstates for spin-1/2 Richardson–Gaudin integrable models”, J. Phys. A: Math. Theor., 55:41 (2022), 415205
Guang-Liang Li, Xiaotian Xu, Kun Hao, Pei Sun, Junpeng Cao, Wen-Li Yang, Kang jie Shi, Yupeng Wang, “Exact solution of the quantum integrable model associated with the twisted D(2)3 algebra”, J. High Energ. Phys., 2022:3 (2022)
Pierre-Antoine Bernard, Nicolas Crampé, Luc Vinet, “Time and band limiting operator and Bethe ansatz”, J. Phys. A: Math. Theor., 55:28 (2022), 285201
Rouven Frassek, István M Szécsényi, “Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin”, J. Phys. A: Math. Theor., 55:50 (2022), 505201
G Niccoli, V Terras, “Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields”, J. Phys. A: Math. Theor., 55:40 (2022), 405203
Arash Jafarizadeh, Mohammad Ali Rajabpour, “Entanglement entropy in quantum spin chains with broken parity number symmetry”, SciPost Phys., 12:6 (2022)
С. Беллиард, Н. А. Славнов, “Перекрытие обычных и модифицированных векторов Бете”, ТМФ, 209:1 (2021), 82–100; S. Belliard, N. A. Slavnov, “Overlap between usual and modified Bethe vectors”, Theoret. and Math. Phys., 209:1 (2021), 1387–1402
Bernard P.-A., Crampe N., Kabakibo D.Sh., Vinet L., “Heun Operator of Lie Type and the Modified Algebraic Bethe Ansatz”, J. Math. Phys., 62:8 (2021), 083501
de Leeuw M., Paletta Ch., Pribytok A., Retore A.L., Torrielli A., “Free Fermions, Vertex Hamiltonians, and Lower-Dimensional Ads/Cft”, J. High Energy Phys., 2021, no. 2, 191
Li G.-L., Xue P., Sun P., Yang H., Xu X., Cao J., Yang T., Yang W.-L., “Exact Solutions of the C-N Quantum Spin Chain”, Nucl. Phys. B, 965 (2021), 115333
Niccoli G. Pei H. Terras V., “Correlation Functions By Separation of Variables: the Xxx Spin Chain”, SciPost Phys., 10:1 (2021), 006
Belliard S. Pimenta R.A. Slavnov N.A., “Scalar Product For the Xxz Spin Chain With General Integrable Boundaries”, J. Phys. A-Math. Theor., 54:34 (2021), 344001
Цитирование в формате AMSBIB
Обратная связь: