Bruno Nachtergaele, The stability of gapped phases and automorphic equivalence
Channel: Scrambled Maths
Date: 08/09/2021

Bruno Nachtergaele, The stability of gapped phases and automorphic equivalence

Abstract:
I discuss the stability of gapped ground state phases of quantum many-body systems under small perturbations of the interactions defining the Hamiltonian. This includes symmetry protected topological phases as well as situations with discrete symmetry breaking. I will review the current status of the problem and then discuss three recent results:
1) the stability of the bulk gap in the presence of gapless edge excitations;
2) stability of the spectral gap in the presence of discrete symmetry breaking:
3) stability of a dimerized phase in a family of quantum spin chains with O(n) symmetry. 
The first two results apply to a general class of frustration-free models on arbitrary lattices. The third is more specialized and deals with a class of one-dimensional systems that are not frustration-free. (Includes joint work with Robert Sims and Amanda Young and with Jakob Bjoernberg, Peter Muehlbacher, and Daniel Ueltschi).

Slides: https://unishare.nl/index.php/s/pHwq3QJwEz9DtLi

Recording of the workshop "Learning from Insulators: New Trends in the Study of Conductivity of Metals". For additional material and information, please consult the workshop page
https://www.lorentzcenter.nl/learning-from-insulators-new-trends-in-the-study-of-conductivity-of-metals.html