P. P. Kulish, N. Manoilovich, Z. Nagy, “Jordanian deformation of the open XXX spin chain”, TMF, 163:2 (2010), 288–298; Theoret. and Math. Phys., 163:2 (2010), 644

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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 163, Number 2, Pages 288–298
DOI: https://doi.org/10.4213/tmf6500 (Mi tmf6500)

This article is cited in 8 scientific papers (total in 9 papers)

Jordanian deformation of the open XXX spin chain

P. P. Kulish^a, N. Manoilovich^b, Z. Nagy^c

^a St. Petersburg Department of Steklov Institute of Mathematics, St.~Petersburg, Russia
^b Departamento de Matemática, Universidade do Algarve, Campus de Gambelas, Faro, Portugal
^c Grupo de Física Mathemática da Universidade de Lisboa, Lisboa, Portugal

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DOI: https://doi.org/10.4213/tmf6500

Abstract: We find the general solution of the reflection equation associated with the Jordanian deformation of the

S L (2)

$SL(2)$ -invariant Yang

R

$R$ -matrix. A special scaling limit of the XXZ model with general boundary conditions leads to the same

K

$K$ -matrix. Following the Sklyanin formalism, we derive the Hamiltonian with the boundary terms in explicit form. We also discuss the structure of the spectrum of the deformed XXX model and its dependence on the boundary conditions.

Keywords: spin chain, boundary condition, quantum group, reflection equation.

Received: 11.11.2009

English version:
Theoretical and Mathematical Physics, 2010, Volume 163, Issue 2, Pages 644–652
DOI: https://doi.org/10.1007/s11232-010-0047-x

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: P. P. Kulish, N. Manoilovich, Z. Nagy, “Jordanian deformation of the open XXX spin chain”, TMF, 163:2 (2010), 288–298; Theoret. and Math. Phys., 163:2 (2010), 644–652

Citation in format AMSBIB

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https://doi.org/10.4213/tmf6500

https://www.mathnet.ru/eng/tmf/v163/i2/p288

This publication is cited in the following 9 articles:

K. R. Atalikov, A. V. Zotov, “Higher-rank generalization of the 11-vertex rational $R$ -matrix: IRF–vertex relations and the associative Yang–Baxter equation”, Theoret. and Math. Phys., 216:2 (2023), 1083–1103
N. Manojlović, I. Salom, “Rational so(3) Gaudin model with general boundary terms”, Nuclear Physics B, 978 (2022), 115747
Kitanine N. Nepomechie R.I. Reshetikhin N., “Quantum Integrability and Quantum Groups: a Special Issue in Memory of Petr P Kulish”, J. Phys. A-Math. Theor., 51:11 (2018), 110201
“Osnovnye nauchnye trudy Petra Petrovicha Kulisha”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 23, Zap. nauchn. sem. POMI, 433, POMI, SPb., 2015, 8–19
N. Cirilo Antonio, N. Manoilovich, Z. Nagy, “Jordanian deformation of the open $s\ell(2)$ Gaudin model”, Theoret. and Math. Phys., 179:1 (2014), 462–471
Antonio N.C., Manojlovic N., Salom I., “Algebraic Bethe Ansatz For the XXX Chain With Triangular Boundaries and Gaudin Model”, Nucl. Phys. B, 889 (2014), 87–108
G. Aminov, S. Arthamonov, A. Smirnov, A. Zotov, “Rational top and its classical $r$ -matrix”, J. Phys. A, 47:30 (2014), 305207–19
Antonio N.C. Manojlovic N. Nagy Z., “Trigonometric Sl (2) Gaudin Model with Boundary Terms”, Rev. Math. Phys., 25:10, SI (2013), 1343004
J. Avan, P. P. Kulish, G. Rollet, “Reflection $K$ -matrices related to Temperley–Lieb $R$ -matrices”, Theoret. and Math. Phys., 169:2 (2011), 1530–1538

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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