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Russian Mathematical Surveys, 2007, Volume 62, Issue 4, Pages 727–766
DOI: https://doi.org/10.1070/RM2007v062n04ABEH004430 (Mi rm6847) 		 
This article is cited in 50 scientific papers (total in 50 papers)

The algebraic Bethe ansatz and quantum integrable systems

N. A. Slavnov

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (652 kB) Citations (50)
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DOI: https://doi.org/10.1070/RM2007v062n04ABEH004430
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 $X\!X\!Z$ Heisenberg chain is considered.
Received: 22.03.2007
Russian version:
Uspekhi Matematicheskikh Nauk, 2007, Volume 62, Issue 4(376), Pages 91–132
DOI: https://doi.org/10.4213/rm6847
Bibliographic databases:
Document Type: Article
UDC: 517.958+530.145
MSC: Primary 82B23; Secondary 81R50, 81U40
Language: English
Original paper language: Russian
Citation: N. A. Slavnov, “The algebraic Bethe ansatz and quantum integrable systems”, Russian Math. Surveys, 62:4 (2007), 727–766
Citation in format AMSBIB
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\paper The algebraic Bethe ansatz and quantum integrable systems
\jour Russian Math. Surveys
\yr 2007
\vol 62
\issue 4
\pages 727--766
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    • This publication is cited in the following 50 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Успехи математических наук Russian Mathematical Surveys
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    Russian version PDF:1006
    English version PDF:44
    References:92
    First page:18
     
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