Jahan A. Claes
Department of Physics
University of Illinois

Abstract: In condensed matter, we assume model Hamiltonians are local. Intuitively, an atom should strongly interact with only its immediate neighbors. In this talk, I’ll give an overview of some of the surprising theorems one can derive for quantum systems based only on the assumption that the Hamiltonian is local. I’ll review known results in this area, including Lieb-Robinson bounds and a lattice version of the Adiabatic theorem, before ultimately presenting a new result on the stability of eigenstates under local perturbations. In the talk, I’ll focus on the intuition and application of the theorems, but I will also sketch a simple proof of the final result.