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Uspekhi Mat. Nauk, 2007, Volume 62, Issue 4(376), Pages 91–132 (Mi umn6847)  

This article is cited in 43 scientific papers (total in 43 papers)

The algebraic Bethe ansatz and quantum integrable systems

N. A. Slavnov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Methods are considered for applying an algebra with bilinear commutation relations to the theory of quantum integrable systems. This survey describes most of the results obtained in this area over the last twenty years, mainly in connection with the computation of correlation functions of quantum integrable systems. Methods for constructing eigenfunctions of the quantum transfer matrix and computing inner products and correlation functions are presented in detail. An example of application of the general scheme to the model of the $XXZ$ Heisenberg chain is considered.


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English version:
Russian Mathematical Surveys, 2007, 62:4, 727–766

Bibliographic databases:

UDC: 517.958+530.145
MSC: Primary 82B23; Secondary 81R50, 81U40
Received: 22.03.2007

Citation: N. A. Slavnov, “The algebraic Bethe ansatz and quantum integrable systems”, Uspekhi Mat. Nauk, 62:4(376) (2007), 91–132; Russian Math. Surveys, 62:4 (2007), 727–766

Citation in format AMSBIB
\by N.~A.~Slavnov
\paper The algebraic Bethe ansatz and quantum integrable systems
\jour Uspekhi Mat. Nauk
\yr 2007
\vol 62
\issue 4(376)
\pages 91--132
\jour Russian Math. Surveys
\yr 2007
\vol 62
\issue 4
\pages 727--766

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    23. Stanislav Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “$GL(3)$-Based Quantum Integrable Composite Models. I. Bethe Vectors”, SIGMA, 11 (2015), 063, 20 pp.  mathnet  crossref  mathscinet  elib
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    35. Mina Aganagic, Andrei Okounkov, “Quasimap counts and Bethe eigenfunctions”, Mosc. Math. J., 17:4 (2017), 565–600  mathnet  crossref
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    38. Maulik D. Okounkov A., “Quantum Groups and Quantum Cohomology”, Asterisque, 2019, no. 408, 1+  crossref  isi
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