Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring
Grzegorz Banaszak, Stefan Barańczuk, Tadeusz Lulek, Jan Milewski, Ryszard Stagraczyński · Acta Physica Polonica A · 2012
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.