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

TL;DR

This paper proves that weak perturbations of non-interacting quantum lattice systems with a gapped ground state lead to the emergence of quasi-particles and develops a scattering theory for these many-particle states.

Contribution

It demonstrates the existence of quasi-particles in perturbed systems and constructs a scattering theory for asymptotically free states.

Findings

Presence of isolated eigenvalues implies quasi-particles

Development of a scattering theory for many-particle states

Perturbations preserve certain spectral features

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.