Some New Approaches of the XXX Heisenberg Model of the Two-Magnon Sector

• Authors: M. Łabuz , J. Milewski , T. Lulek
• Languages of publication: EN

Abstracts

EN

XXX Heisenberg s-1/2 model has been examined in detail during last decades, however, recently one may find some new insights into that issue. Among several approaches describing the eigenproblem for the finite case, a close look into the structure of Bethe equations (BE) for the two-magnon sector case seems to be particularly interesting. BE enable us to evaluate parameters labeling eigenstates of a magnet, however to find appropriate sets of winding numbers, which parametrize BE, one has to apply the Inverse Bethe Ansatz method. On the other hand, one may choose a different - combinatoric approach - which also parametrizes Bethe eigenstates, with the use of rigging numbers describing string configurations. We present an idea of comparison of the concepts mentioned above for the particular case of two-spin deviations sector.

Keywords

EN

75.10.Jm; 03.65.Fd; 03.67.Lx; 02.10.Ud; 02.10.De

Discipline

• 02.10.Ud: Linear algebra
• 03.65.Fd: Algebraic methods(see also 02.20.-a Group theory)
• 02.10.De: Algebraic structures and number theory
• 03.67.Lx: Quantum computation architectures and implementations
• 75.10.Jm: Quantized spin models, including quantum spin frustration

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2018
• Volume: 133
• Issue: 3
• Pages: 444-446

Dates

published

2018-03

Contributors

author

M. Łabuz

• Department of Theoretical Physics, Faculty of Mathematics and Natural Sciences, University of Rzeszow, Πgonia 1, 35-310 Rzeszów, Poland

author

J. Milewski

• Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland

author

T. Lulek

• Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland and East European State University in Przemyśl, Książąt Lubomirskich 6, 37-700 Przemyśl, Poland

References

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• [4] W.J. Caspers, A. Wal, M. Łabuz, M. Kuźma, T. Lulek: J. Math. Phys. 45, 391 (2004), doi: 10.1063/1.1623614
• [5] H. Bethe: Z. Physik 71, 205 (1931) doi: 10.1007/BF01341708 (in German) English translation in: D.C. Mattis, The Many-Body Problem, World Sci., Singapore 1993, p. 689, doi: 10.1142/9789812796523
• [6] J. Milewski, G. Banaszak, T. Lulek, M. Labuz, Physica B 406, 520 (2011), doi: 10.1016/j.physb.2010.11.027
• [7] T. Lulek: Banach Center Publications 78, 231 (2007), doi: 10.4064/bc78-0-17
• [8] S. Dasmahapatra, O. Foda: Int. J. Mod. Phys. A 38, 1041 (1997), doi: 10.1142/S0217751X98000214

Identifiers

DOI

10.12693/APhysPolA.133.444