Abstract

The topological classification of hermitian operators is solely determined by the presence or absence of certain discrete symmetries. Non-hermitian systems not only admit more types of discrete symmetries, their spectrum is a subset of the complex plane. Hence, spectral gaps come in two flavors and we in addition need to specify whether we are dealing with a point gap (co-dimension 2) or a line gap (co-dimension 1). Since the presence of a line gap implies the existence of a point gap, there is usually more than one mathematical classification of a physical system. To decide which classification is physically meaningful, I propose a simple physical criterion based on the notion of physically relevant states. This generalizes of the notion of Fermi projection, which even in the hermitian case not determines the topological bulk classification of fermionic condensed matter systems, but enters as an auxiliary quantity in the topological classification of photonic and magnonic crystals. A crucial point in my investigation is the relevance of diagonalizability in topological classifications, i. e. the absence of Jordan blocks.

This talk will be held online using Zoom. Please register your email address here to receive Zoom links via email.

Workshop website: https://www.mtg.msm.cam.ac.uk/events/msm-aimr-joint-online-workshop-2020