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Point Group Interpretation of Galois Symmetry of Bethe Ansatz Solutions of Magnetic Pentagonal Ring

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Lulek B., Lulek T., Łabuz M., Milewski J.

Acta Physica Polonica A

2015

vol. 127

issue 2

336-338

Exact solutions of the eigenproblem of the magnetic pentagonal ring exhibit the arithmetic symmetry expressed in terms of a Galois group of a finite extension of the prime field Q of rationals. We propose here a geometric interpretation of this symmetry in the interior of the Brillouin zone, in terms of point groups. Explicitly, it is a subgroup of the direct product C₄ × D₄. We present also the appropriate irreducible representations of the group.

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

100%

Łabuz M., Milewski J., Lulek T.

Acta Physica Polonica A

2018

vol. 133

issue 3

444-446

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.

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2 Acta Physica Polonica A

1 2018

1 2015

2 Lulek T.

2 Milewski J.

2 Łabuz M.

1 Lulek B.

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Point Group Interpretation of Galois Symmetry of Bethe Ansatz Solutions of Magnetic Pentagonal Ring

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