Analysis of a family of Heisenberg systems with simple eigenfunctions for the ground state and low lying excitations

Abstract

We analyze a family of one and bi-dimensional frustrated Heisenberg systems, whose ground state (GS) and low lying excitation spectrum can be exactly described as a product. The magnetic lattice is composed by clusters of spin $S$ ions. These clusters are connected to each other by intermediate, spin $\ensuremath{\sigma}$ ions (here called ``connectors''). The value of $S$ and $\ensuremath{\sigma}$ are arbitrary. Three major properties of these systems are: (i) The GS is exponentially degenerate. (ii) The low lying excitations are separated from the GS by a gap, and they are localized. However, neighbor excitations interact, exchanging energy; two ``bottom'' excitations repel each other. (iii) The magnetization curve has a staircaselike form. On introducing a direct connector-connector coupling, a break in the lattice translational symmetry can occur, due to the uniform magnetic field. Finally, we study the effect of a weak departure from the hypothesis of the model, with the aim to make it more adaptable to fit different actual magnetic systems. We obtain bands of delocalized excitations. Bounded states between excitations also appear.