Special CPM Seminar

Why the band structure of non-Hermitian Hamiltonians can lie to you and what to do about it

Alexander McDonald

Université de Sherbrooke

In recent years, there has been considerable theoretical and experimental interest in studying how non-Hermitan Hamiltonians, that is systems whose dynamical matrix is non-Hermitian, differ from their usual Hermitian counterparts. Perhaps the most unusual phenomenon exhibited by non-Hermitian tight-binding models is the so-called non-Hermitian skin effect (NHSE) where a “macroscopic” number of edge modes appear when going from periodic to open boundary conditions. Given the wealth of information provided by the band structure in a conventional Hermitian setting, much effort has been spent in understanding this anomalous sensitivity to boundary conditions.

In this talk I will argue that in models exhibiting the NHSE, the band structure of open-boundary systems often provides little to no information about relevant physical quantities of interest; the band structure lies to you about relevant length and timescales. By constructing fully quantum-mechanically-consistent models exhibiting the NHSE, I will discuss why this must be the case. Finally, I will demonstrate how to identify the correct length and timescales present in such systems.