No abstract

No abstract

We analyse the exact solution of the eigenproblem for the Heisenberg Hamiltonian of magnetic heptagon, i.e. the ring of N = 7 nodes, each with spin 1/2, within the XXX model with nearest neighbour interactions, from the point of view of finite extensions of the field Q of rationals. We point out, as the main result, that the associated arithmetic structure of these extensions makes natural an introduction of some Galois qubits. They are two-dimensional subspaces of the Hilbert space of the model, which admit a quantum informatic interpretation as elementary memory units for a (hypothetical) computer, based on their distinctive properties with respect to the action of related Galois group for indecomposable factors of the secular determinant.These Galois qubits are nested on the lattice of subfields which involves several minimal fields for determination of eigenstates (the complex Heisenberg field), spectrum (the real Heisenberg field), and Fourier transforms of magnetic configurations (the cyclotomic field, based on the simple 7th root of unity). The structure of the corresponding lattice of Galois groups is presented in terms of Kummer theory, and its physical interpretation is indicated in terms of appropriate permutations of eigenstates, energies, and density matrices. Exemplary OSID style[J. Milewski et al., Galois actions on the eigenproblem of the Heisenberg heptagon] 2 Kummer theory.

Bethe solutions for r reversed spins are characterized by a set of winding numbers {λ1⩽λ2⩽⋯⩽λr}. Such classification is, however, not unique since the same sequences can describe different solutions and different sequences yield essentially equivalent states. These ambiguities should find their resolution in a complete configuration. We demonstrate here that in general a solution with a fixed sequence of winding numbers evolves in a quasicontinuous way as the function of N, the number of spins. This property could be disturbed in some cases at special transition point Ntr. We explain analytically the origin of this discontinuity. Consideration was addressed for three and four spin deviations.

No abstract

No abstract

The energy spectra of short rings of spin S = 1/2 particles with a nearest neighbour Heisenberg interaction have features which are common for various numbers N of spins. The example of N = 8 was considered in detail, for which a complete set of eigenstates and eigenvalues is obtained by the Bethe Ansatz model. The results were compared with the rotational band model usually used for the interpretation of experimental data for antiferromagnetic molecular magnets.

No abstract