Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring

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