Modul:   MAT675  PDE and Mathematical Physics

Spectral gaps and spectral gap stability for quantum lattice systems

Vortrag von Prof. Dr. Bruno Nachtergaele

Sprecher eingeladen von: Prof. Dr. Benjamin Schlein

Datum: 01.12.22  Zeit: 16.00 - 18.00  Raum: KOL G209

A salient feature of topological insulators and symmetry protected topological phases of quantum lattice systems is the spectral gap above the ground state. I will review recent results of two types. The first are proofs of lower bounds for the spectral gap for a variety of specific models. The second type of results is concerned with the stability of the spectral gap and other fundamental characteristics of the system under uniformly small perturbations of the interactions in the model Hamiltonian. I will discuss the basic strategies used to approach both types of problems.