Heisenberg and Bethe Field Extensions Applied to Magnetic Rings

Abstract

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 especially applications of Galois theory for computation of the spectrum of the Heisenberg operators and Bethe parameters. The solutions of the Heisenberg eigenproblem and Bethe Ansatz generate interesting families of algebraic number fields. Galois theory yields additional symmetries which not only simplify the analysis of the model but may lead to new applications and horizons.

Three-Diagonal Blocks of Two-Magnon Hamiltonians with Specified Wave Numbers for Heisenberg Rings

“…[2][3][4][5][6][7]. As matrix elements of the Heisenberg Hamiltonian are of the arithmetic form [8], solutions of the eigenproblem reveal the Galois symmetry [9][10][11].…”