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

M. Łabuza, J. Milewskib and T. Lulekc aDepartment of Theoretical Physics, Faculty of Mathematics and Natural Sciences, University of Rzeszow, Pigonia 1, 35-310 Rzeszów, Poland bInstitute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland cFaculty 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

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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.

DOI: 10.12693/APhysPolA.133.444 PACS numbers: 75.10.Jm, 03.65.Fd, 03.67.Lx, 02.10.Ud, 02.10.De