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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.

Bethe Ansatz and Geometry of the Classical Configuration Space

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Lulek B., Lulek T., Milewski J.

Acta Physica Polonica A

2009

vol. 115

issue 1

159-161

We demonstrate that the seminal one-dimensional model of the Heisenberg magnet, consisting of N spins 1/2 with the nearest-neighbour isotropic interaction, solved exactly by Bethe ansatz, admits an interpretation of a system of r=N/2-M pseudoparticles (spin deviations) which are indistinguishable, have hard cores and move on the chain by local hoppings. Such an approach allows us to construct a manifold with some boundaries, which is genericly r-dimensional, and whose F-dimensional regions, 0

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2 Acta Physica Polonica A

1 2015

1 2009

2 Lulek B.

2 Lulek T.

2 Milewski J.

1 Łabuz M.

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

Bethe Ansatz and Geometry of the Classical Configuration Space