Perturbations of ground states in weakly interacting quantum spin systems.

We consider a general weak bounded finite range perturbation of a general free quantum spin Hamiltonian on a lattice. We prove that if the free Hamiltonian has a nondegenerate ground state and a spectral gap, then the perturbation also has a ground state, and estimate the localization of the spectrum in the corresponding ground state representation. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]