Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring

Abstract

We analyse the number eld-theoretic properties of solutions of the eigenproblem of the Heisenberg Hamiltonian for the magnetic hexagon with the single-node spin 1/2 and isotropic exchange interactions. It follows that eigenenergies and eigenstates are expressible within an extension of the prime eld Q of rationals of degree 2 3 and 2 4 , respectively. In quantum information setting, each real extension of rank 2 represents an arithmetic qubit. We demonstrate in detail some actions of the Galois group on the eigenproblem.

Heisenberg and Bethe Field Extensions Applied to Magnetic Rings

“…For the last 10 years a new method of investigating Quantum Mechanics in the context of Bethe Ansatz for the magnetic homogeneous ring has been introduced in the papers [1][2][3][4]. The idea of this new method is based on the observation that the Heisenberg Hamiltonian is an arithmetic operator.…”