In this paper the field generated by the Bethe parameters related to the XXX model for the
Heisenberg pentagon is considered. For the interior of the Brillouin zone, the Galois group of …

A method of separation of subspaces with definite values of the total spin, its z-projection
and quasimomentum, within the state space of the XXX model, ie the N-th tensor power of a …

The exact Bethe eigenfunctions for the heptagonal ring within the isotropic XXX model
exhibit a doubly degenerated energy level in the three-deviation sector at the centre of the …

We consider the factor υ of the characteristic polynomial w H (x) of the Heisenberg
Hamiltonian Ĥ of the XXX model, corresponding to the generic star [k=±1,±3] of …

Galois symmetry of exact Bethe Ansatz eigenstates for the magnetic pentagonal ring within
the XXX model are investigated by a comparison with crystallographic constructions of …

An arithmetic qubit, separated from the state space of the heptagonal magnetic ring within
the XXX model in the three-magnon sector at the center of the Brillouin zone, is shown to …

We consider striking connections between the theory of homogenous isotropic Heisenberg
ring (XXX-model) and algebraic number theory. We explain the nature of these connections …

We demonstrate some applications of arithmetic structures in Bethe Ansatz—the famous
substitution which yields an exact solution of a quantum N-body problem for the linear …

In 1931 Hans Bethe introduced his famous ansatz concerning the diagonalization of the
Heisenberg Hamiltonian of a ring consisting of N nodes [1]. However, Bethe ansatz …

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 …