V. O. Tarasov, “Irreducible monodromy matrices for the $R$ matrix of the $XXZ$ model and local lattice quantum Hamiltonians”, TMF, 63:2 (1985), 175–196; Theoret. and Math. Phys., 63:2 (1985), 440

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Teoreticheskaya i Matematicheskaya Fizika, 1985, Volume 63, Number 2, Pages 175–196 (Mi tmf4754)

This article is cited in 77 scientific papers (total in 77 papers)

Irreducible monodromy matrices for the

$R$ matrix of the

$XXZ$ model and local lattice quantum Hamiltonians

V. O. Tarasov

Full-text PDF (2281 kB) Citations (77)

References:

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Abstract: Monodromy matrices with vacuum and finite-dimensional single-particle subspace are considered for the

$R$ matrices of the

$XXX$ and

$XXZ$ models. A natural class of monodromy matrices – irreducible monodromy matrices – is described; for these matrices, the propositions proposed earlier as natural hypotheses are valid. The existence of local Hamiltonians is proved for quantum integrable models on a lattice with irreducible local monodromy matrices.

Received: 23.05.1984

English version:
Theoretical and Mathematical Physics, 1985, Volume 63, Issue 2, Pages 440–454
DOI: https://doi.org/10.1007/BF01017900

Bibliographic databases:

Language: Russian

Citation: V. O. Tarasov, “Irreducible monodromy matrices for the

$R$ matrix of the

$XXZ$ model and local lattice quantum Hamiltonians”, TMF, 63:2 (1985), 175–196; Theoret. and Math. Phys., 63:2 (1985), 440–454

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

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Linking options:

https://www.mathnet.ru/eng/tmf4754

https://www.mathnet.ru/eng/tmf/v63/i2/p175

This publication is cited in the following 77 articles:

Hao Chang, Jinxin Hu, Lewis Topley, “Modular representations of the Yangian Y2$Y_2$”, Journal of London Math Soc, 111:1 (2025)
Samuel Belliard, Rodrigo Alves Pimenta, Nikita A. Slavnov, “Modified rational six vertex model on the rectangular lattice”, SciPost Phys., 16:1 (2024), 9–20
A. I. Molev, “Representations of the Yangians Associated with Lie Superalgebras $\mathfrak {osp}(1|2n)$”, Commun. Math. Phys., 398:2 (2023), 541
Slaven Kožić, “On the h-adic Quantum Vertex Algebras Associated with Hecke Symmetries”, Commun. Math. Phys., 397:2 (2023), 607
A. I. Molev, “Odd reflections in the Yangian associated with $\mathfrak {gl}(m|n)$”, Lett Math Phys, 112:1 (2022)
D. Karakhanyan, R. Kirschner, “Representations of orthogonal and symplectic Yangians”, Nuclear Physics B, 967 (2021), 115402
Naihuan Jing, Ming Liu, Alexander Molev, “Isomorphism between the $R$-Matrix and Drinfeld Presentations of Quantum Affine Algebra: Types $B$ and $D$”, SIGMA, 16 (2020), 043, 49 pp.
Naihuan Jing, Ming Liu, Alexander Molev, “Representations of Quantum Affine Algebras in their $R$-Matrix Realization”, SIGMA, 16 (2020), 145, 25 pp.
Naihuan Jing, Ming Liu, Alexander Molev, “Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: Type C”, Journal of Mathematical Physics, 61:3 (2020)
Shi-Yao Hou, Ningping Cao, Sirui Lu, Yi Shen, Yiu-Tung Poon, Bei Zeng, “Determining system Hamiltonian from eigenstate measurements without correlation functions”, New J. Phys., 22:8 (2020), 083088
Stukopin V., Xxv International Conference on Integrable Systems and Quantum Symmetries (Isqs-25), Journal of Physics Conference Series, 965, IOP Publishing Ltd, 2018
Nicolas Guay, Vidas Regelskis, Curtis Wendlandt, “Twisted Yangians of small rank”, Journal of Mathematical Physics, 57:4 (2016)
S. Belliard, R.A. Pimenta, “Modified algebraic Bethe ansatz for XXZ chain on the segment – II – general cases”, Nuclear Physics B, 894 (2015), 527
Samuel Belliard, “Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases”, Nuclear Physics B, 892 (2015), 1
M. Wheeler, “Scalar Products in Generalized Models with SU(3)-Symmetry”, Commun. Math. Phys., 327:3 (2014), 737
D Chicherin, S Derkachov, “The R-operator for a modular double”, J. Phys. A: Math. Theor., 47:11 (2014), 115203
Sergey Khoroshkin, Maxim Nazarov, Alexander Shapiro, “Rational and polynomial representations of Yangians”, Journal of Algebra, 418 (2014), 265
V. A. Stukopin, “Representations of the Yangian of a Lie superalgebra of type $A(m,n)$”, Izv. Math., 77:5 (2013), 1021–1043
Vladimir Stukopin, “On representations of Yangian of Lie SuperalgebraA(n,n) type”, J. Phys.: Conf. Ser., 411 (2013), 012027
Sachin Gautam, Valerio Toledano Laredo, “Yangians and quantum loop algebras”, Sel. Math. New Ser., 19:2 (2013), 271

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

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