Toeplitz algebras and spectral results for the one-dimensional   Heisenberg model
  We determine the structure of the spectrum and obtain non-propagation estimates for a class of Toeplitz operators acting on a subset of the lattice $\Z^N$. This class contains the Hamiltonian of the one-dimensional Heisenberg model. 
Mondher Damak, Marius Mantoiu, Rafael Tiedra de Aldecoa