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Group Actions and Classification of Quantum States of the Heisenberg Model of Magnetism

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Algebraic Combinatorics and Applications

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Abstract

The kinematics and dynamics of the Heisenberg model of magnetism is reviewed from the point of view of combinatorics. The general scheme of the duality of Weyl is presented at two levels: (i) the total space of all quantum states of the magnet, (ii) the subspace with the definite number of spin deviations. The role of dual actions of appropriate groups is emphasised and the corresponding quantum numbers are pointed out.

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References

  1. W. Heisenberg, Z. Phys. 49, 619 (1928)

    Article  MATH  Google Scholar 

  2. D.C. Mattis, The Theory of Magnetism, Springer Berlin 1981.

    Google Scholar 

  3. H. Weyl, The Theory of Groups and Quantum Mechanics, Princeton 1931.

    Google Scholar 

  4. W. Pauli, Z. Phys. 31, 765 (1925)

    Article  MATH  Google Scholar 

  5. H. Bethe, Z. Phys. 71, 205 (1931) (English translation in [6])

    Google Scholar 

  6. D.C. Mattis, An Encyclopedia of Exactly Solved Models in One Dimension, World Sci., Singapore 1993, pp. 689 - 716.

    MATH  Google Scholar 

  7. L.A. Takhtajan, Phys. Lett. 87A, 479 (1982)

    Article  MathSciNet  Google Scholar 

  8. S.V. Kerov, A.N. Kirillov, and N.Yu. Reshetikhin, J. Sov. Math. 41, 916 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  9. A.N. Kirillov and N.Yu. Reshetikhin, J. Sov. Math. 41, 925 (1998).

    Article  MathSciNet  Google Scholar 

  10. A.N. Kirillov and N.Yu. Reshetikhin, Lett. Math. Phys. 12, 199 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  11. A.N. Kirillov, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 131, 88 (1983).

    MathSciNet  Google Scholar 

  12. A. Lascoux, B. Leclerc, and J.-Y. Thibon, J. Math. Phys. 38, 1041 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  13. S. Dasmahapatra and O. Foda, Int. J. Mod. Phys. A13, 501 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  14. A. Schilling and S.O. Warnaar, Commun. Math. Phys. 202, 359 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  15. B. Lulek and T. Lulek, Rep. Math. Phys. 38, 277 (1996)

    Google Scholar 

  16. B. Lulek and T. Lulek, J. Phys. A.: Math. Gen. 29, 4687 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  17. B. Lulek and T. Lulek, Rep. Math. Phys. 38, 267 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  18. B. Lulek, Acta Phys. Polon. B22, 371 (1991)

    MathSciNet  Google Scholar 

  19. B. Lulek, J. Phys: Condens. Matter 4, 8737 (1992)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Physics, Pedagogical University, ul. Rejtana 16A, 35-359, Rzeszów, Poland

    Tadeusz Lulek

Authors
  1. Tadeusz Lulek
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Editor information

Editors and Affiliations

  1. Lehrstuhl II für Mathematik, Universität Bayreuth, 95440, Bayreuth, Germany

    Anton Betten , Axel Kohnert , Reinhard Laue  & Alfred Wassermann , ,  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Lulek, T. (2001). Group Actions and Classification of Quantum States of the Heisenberg Model of Magnetism. In: Betten, A., Kohnert, A., Laue, R., Wassermann, A. (eds) Algebraic Combinatorics and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59448-9_17

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  • DOI: https://doi.org/10.1007/978-3-642-59448-9_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41110-9

  • Online ISBN: 978-3-642-59448-9

  • eBook Packages: Springer Book Archive

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