The Galois symmetry of exact Bethe Ansatz eigenstates for magnetic pentagonal ring is shown to bear a close analogy to some crystallographic constructions.Automorphisms of number field extensions associated with these eigenstates prove to be related to choices of the Bravais cells in the finite crystal lattice Z2 × Z2, responsible for extension of the cyclotomic field by the Bethe parameters.

Acta Physica Polonica AJul 1, 20170 citations

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

Barbara Lulek, Tadeusz Lulek, M. Łabuz +1 more

Exact solutions of the eigenproblem of the magnetic pentagonal ring exhibit the arithmetic symmetry expressed in terms of a Galois group of a nite extension of the prime eld 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.

Acta Physica Polonica AFeb 1, 20150 citations