Quasi-particles in weak perturbations of non-interacting quantum lattice systems

Abstract

We consider a general weak perturbation of a non-interacting quantum lattice system with a non-degenerate gapped ground state. We prove that the presence of isolated eigenvalues in the spectrum of the decoupled model leads to the existence of quasi-particles in the perturbed model. Also, a scattering theory for asymptotically free many-particle states is developed.