Speaker: Alexander Mc Donald
Affiliation: Universidad de Chicago
Date: Tuesday, 14 June 2022 at 15:00
Location: Seminar Room, Serrano 113b
Non-Hermitian lattice models have received an enormous amount of attention in recent years, in part because they violate seemingly-obvious intuition found in any Hermitian model. The paradigmatic example is the non-Hermitian skin effect (NHSE), in which a non-Hermitian Hamiltonian exhibits a striking sensitivity to boundary conditions; the spectrum and eigenvectors under open boundary conditions in no way resembles its periodic system counterpart. While the dynamics of such models have received some attention, the same can not be said for the stationary states of such models. This is especially relevant in a quantum setting, where dissipation used to realize non-Hermiticity must be accompanied by unavoidable fluctuations.In this talk, I will discuss how a generic non-Hermitian tight-binding model can be realized in a quantum-mechanically consistent manner by constructing an appropriate open quantum system. Focusing on a quantum realization of the Hatano-Nelson model, I will demonstrate how the non-Hermitian skin effect alone cannot be used to predict relevant steady-state properties. I will instead argue that propagation physics, as encoded by the systems Green’s function, is the relevant object that controls the steady state. Using this quantity, we are able to understand both why the steady state occupation is controlled by a macroscopic length scale and why this real-space density is markedly different for bosons versus fermions. How work highlights the importance of characterizing a non-Hermitian Hamiltonian beyond its eigenvalues and eigenvectors.