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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 104, Number 1, Pages 8–24 (Mi tmf1321)  
This article is cited in 12 scientific papers (total in 12 papers)

Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems

A. V. Zabrodinab

a N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
Full-text PDF (1795 kB) Citations (12)
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Abstract: We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension are identified with traces of quantum monodromy matrices for specific integrable systems with non-periodic boundary conditions. Applications to the Azbel–Hofstadter problem are outlined.
English version:
Theoretical and Mathematical Physics, 1995, Volume 104, Issue 1, Pages 762–776
DOI: https://doi.org/10.1007/BF02066651
Bibliographic databases:
Language: English
Citation: A. V. Zabrodin, “Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems”, TMF, 104:1 (1995), 8–24; Theoret. and Math. Phys., 104:1 (1995), 762–776
Citation in format AMSBIB
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\by A.~V.~Zabrodin
\paper Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems
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\vol 104
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\pages 8--24
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1602858}
\zmath{https://zbmath.org/?q=an:0855.58039}
\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 104
\issue 1
\pages 762--776
\crossref{https://doi.org/10.1007/BF02066651}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TX90500002}
Linking options:
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  • https://www.mathnet.ru/eng/tmf/v104/i1/p8
    • This publication is cited in the following 12 articles:
    1. Pascal Baseilhac, Rodrigo A. Pimenta, “Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz”, Nuclear Physics B, 949 (2019), 114824  crossref
    2. N. Manojlović, I. Salom, “Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model”, Nuclear Physics B, 923 (2017), 73  crossref
    3. Liyan Liu, Qinghai Hao, “Planar hydrogen-like atom in inhomogeneous magnetic fields: Exactly or quasi-exactly solvable models”, Theoret. and Math. Phys., 183:2 (2015), 730–736  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. Aneva B., “Exact solvability of interacting many body lattice systems”, Physics of Particles and Nuclei, 41:4 (2010), 471–507  crossref  isi
    5. Doikou, A, “A note on the boundary spin s XXZ chain”, Physics Letters A, 366:6 (2007), 556  crossref  mathscinet  adsnasa  isi
    6. Baseilhac, P, “The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach”, Nuclear Physics B, 754:3 (2006), 309  crossref  mathscinet  zmath  adsnasa  isi
    7. Doikou, A, “The open XXZ and associated models at q root of unity”, Journal of Statistical Mechanics-Theory and Experiment, 2006, P09010  crossref  mathscinet  isi
    8. Bajnok, Z, “From defects to boundaries”, International Journal of Modern Physics A, 21:5 (2006), 1063  crossref  mathscinet  zmath  adsnasa  isi
    9. Doikou, A, “From affine Hecke algebras to boundary symmetries”, Nuclear Physics B, 725:3 (2005), 493  crossref  mathscinet  zmath  adsnasa  isi
    10. Baseilhac, P, “A new (in)finite-dimensional algebra for quantum integrable models”, Nuclear Physics B, 720:3 (2005), 325  crossref  mathscinet  zmath  adsnasa  isi
    11. Baseilhac, P, “Deformed Dolan-Grady relations in quantum integrable models”, Nuclear Physics B, 709:3 (2005), 491  crossref  mathscinet  zmath  adsnasa  isi
    12. Arnaudon, D, “Analytical Bethe ansatz for closed and open gl(N)-spin chains in any representation”, Journal of Statistical Mechanics-Theory and Experiment, 2005, P02007  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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