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TMF, 1983, Volume 57, Number 2, Pages 163–181 (Mi tmf2251)  

This article is cited in 29 scientific papers (total in 30 papers)

Local Hamiltonians for integrable quantum models on a lattice

V. O. Tarasov, L. A. Takhtadzhyan, L. D. Faddeev


Abstract: A general method is proposed for constructing local Hamiltonians for integrable lattice models. These Hamiltonians are diagonalized for the case of a two-dimensional auxiliary space. The Heisenberg XXX model and the lattice model of the nonlinear Schrödinger equation are considered in detail.

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English version:
Theoretical and Mathematical Physics, 1983, 57:2, 1059–1073

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Received: 15.04.1983

Citation: V. O. Tarasov, L. A. Takhtadzhyan, L. D. Faddeev, “Local Hamiltonians for integrable quantum models on a lattice”, TMF, 57:2 (1983), 163–181; Theoret. and Math. Phys., 57:2 (1983), 1059–1073

Citation in format AMSBIB
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\by V.~O.~Tarasov, L.~A.~Takhtadzhyan, L.~D.~Faddeev
\paper Local Hamiltonians for integrable quantum models on a~lattice
\jour TMF
\yr 1983
\vol 57
\issue 2
\pages 163--181
\mathnet{http://mi.mathnet.ru/tmf2251}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=734882}
\transl
\jour Theoret. and Math. Phys.
\yr 1983
\vol 57
\issue 2
\pages 1059--1073
\crossref{https://doi.org/10.1007/BF01018648}
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    This publication is cited in the following articles:
    1. N. M. Bogolyubov, A. G. Izergin, “Lattice completely integrable regularization of the sine-Gordon model for small coupling constants”, Theoret. and Math. Phys., 59:2 (1984), 441–452  mathnet  crossref  mathscinet  isi
    2. M. V. Karasev, V. P. Maslov, “Asymptotic and geometric quantization”, Russian Math. Surveys, 39:6 (1984), 133–205  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. N. M. Bogolyubov, A. G. Izergin, “Lattice sine-Gordon model with local Hamiltonian”, Theoret. and Math. Phys., 61:3 (1984), 1195–1204  mathnet  crossref  mathscinet  isi
    4. V. O. Tarasov, “Local Hamiltonians for integrable quantum models on a lattice. II”, Theoret. and Math. Phys., 61:3 (1984), 1211–1215  mathnet  crossref  mathscinet  isi
    5. N. Yu. Reshetikhin, “Integrable models of quantum one-dimensional magnets with $O(n)$ and $Sp(2k)$ symmetry”, Theoret. and Math. Phys., 63:3 (1985), 555–569  mathnet  crossref  mathscinet  isi
    6. V. O. Tarasov, “Irreducible monodromy matrices for the $R$ matrix of the $XXZ$ model and local lattice quantum Hamiltonians”, Theoret. and Math. Phys., 63:2 (1985), 440–454  mathnet  crossref  mathscinet  isi
    7. A. A. Vladimirov, “Proof of the invariance of the Bethe-ansatz solutions under complex conjugation”, Theoret. and Math. Phys., 66:1 (1986), 102–105  mathnet  crossref  mathscinet  isi
    8. N. M. Bogolyubov, V. E. Korepin, “Quantum nonlinear Schrödinger equation on a lattice”, Theoret. and Math. Phys., 66:3 (1986), 300–305  mathnet  crossref  mathscinet  isi
    9. M. V. Karasev, “Analogues of the objects of Lie group theory for nonlinear Poisson brackets”, Math. USSR-Izv., 28:3 (1987), 497–527  mathnet  crossref  mathscinet  zmath
    10. N. M. Bogolyubov, “Thermodynamics of a one-dimensional lattice Bose gas”, Theoret. and Math. Phys., 67:3 (1986), 614–622  mathnet  crossref  mathscinet  isi
    11. L. V. Avdeev, A. A. Vladimirov, “Exceptional solutions to the Bethe ansatz equations”, Theoret. and Math. Phys., 69:2 (1986), 1071–1079  mathnet  crossref  mathscinet  isi
    12. N. M. Bogolyubov, A. G. Izergin, V. E. Korepin, “Critical exponents in completely integrable models of quantum statistical physics”, Theoret. and Math. Phys., 70:1 (1987), 94–102  mathnet  crossref  mathscinet  isi
    13. A. Yu. Volkov, L. D. Faddeev, “Quantum inverse scattering method on a spacetime lattice”, Theoret. and Math. Phys., 92:2 (1992), 837–842  mathnet  crossref  mathscinet  isi
    14. A. Kundu, “Classical integrable lattice models through quantum group related formalism”, Theoret. and Math. Phys., 99:3 (1994), 699–704  mathnet  crossref  mathscinet  zmath  isi
    15. Yu. S. Osipov, A. A. Gonchar, S. P. Novikov, V. I. Arnol'd, G. I. Marchuk, P. P. Kulish, V. S. Vladimirov, E. F. Mishchenko, “Lyudvig Dmitrievich Faddeev (on his sixtieth birthday)”, Russian Math. Surveys, 50:3 (1995), 643–659  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. A. V. Antonov, “Quantum Volterra model and universal $R$-matrix”, Theoret. and Math. Phys., 113:3 (1997), 1520–1529  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. Hikami, K, “The Z(N) symmetric quantum lattice field theory the quantum group symmetry, the Yang–Baxter equation, and the integrals of motion”, Journal of the Physical Society of Japan, 68:1 (1999), 55  crossref  isi
    18. L. N. Lipatov, “Integrability properties of high energy dynamics in the multi-color QCD”, Phys. Usp., 47:4 (2004), 325–339  mathnet  crossref  crossref  adsnasa  isi
    19. D. R. Karakhanyan, “Constructing Representations of the Nonstandardly Deformed Algebra $s\ell_\xi(2)$”, Theoret. and Math. Phys., 138:2 (2004), 177–189  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    20. A. S. Gorsky, “Gauge theories as string theories: the first results”, Phys. Usp., 48:11 (2005), 1093–1108  mathnet  crossref  crossref  adsnasa  isi
    21. N. M. Bogolyubov, K. L. Malyshev, “Ising limit of a Heisenberg $XXZ$ magnet and some temperature correlation functions”, Theoret. and Math. Phys., 169:2 (2011), 1517–1529  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    22. Chicherin D., Derkachov S., Karakhanyan D., Kirschner R., “Baxter operators for arbitrary spin II”, Nuclear Phys B, 854:2 (2012), 433–465  crossref  isi
    23. Grosjean N. Maillet J.-M. Niccoli G., “On the Form Factors of Local Operators in the Bazhanov-Stroganov and Chiral Potts Models”, Ann. Henri Poincare, 16:5 (2015), 1103–1153  crossref  isi
    24. N. A. Slavnov, “One-dimensional two-component Bose gas and the algebraic Bethe ansatz”, Theoret. and Math. Phys., 183:3 (2015), 800–821  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    25. S. E. Derkachov, D. I. Chicherin, “Matrix factorization for solutions of the Yang–Baxter equation”, J. Math. Sci. (N. Y.), 213:5 (2016), 723–742  mathnet  crossref  mathscinet
    26. N. M. Bogolyubov, K. L. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70:5 (2015), 789–856  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    27. Dmitry Chicherin, Sergey E. Derkachov, Vyacheslav P. Spiridonov, “From Principal Series to Finite-Dimensional Solutions of the Yang–Baxter Equation”, SIGMA, 12 (2016), 028, 34 pp.  mathnet  crossref
    28. D. R. Karakhanyan, R. Kirshner, “Second-order evaluations of orthogonal and symplectic Yangians”, Theoret. and Math. Phys., 192:2 (2017), 1154–1161  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    29. N. M. Belousov, S. E. Derkachev, “$Q$-operator dlya kvantovoi modeli NSh”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 25, K 70-letiyu M. A. Semenova-Tyan-Shanskogo, Zap. nauchn. sem. POMI, 473, POMI, SPb., 2018, 34–65  mathnet
    30. D. R. Karakhanyan, R. Kirshner, “Orthogonal and symplectic Yangians and Lie algebra representations”, Theoret. and Math. Phys., 198:2 (2019), 239–248  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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