Modelling the Onset of the Selective Non-Hermitian Skin Effect

Within the standard Hermitian framework of quantum physics, lattice systems are generally described using periodic boundary conditions where lattice edges can be ignored and eigenstates are distributed within the bulk. This framework, however, fails to capture the behavior of open systems where dissipative effects are relevant. In this context, dramatically different behavior can be observed at the lattice edges than within the bulk. We will consider how these novel edge effects can be captured using a non-Hermitian Hamiltonian under open boundary conditions and introduce our model for what is known as the selective non-Hermitian skin effect.

We begin by considering the Hatano–Nelson (HN) model, a non-Hermitian tight-binding model which allows for asymmetric couplings between adjacent lattice sites and causes bulk eigenstates to be localized near boundaries by the so-called non-Hermitian skin effect. We then present an extension of the HN model known as the selective non-Hermitian skin effect which introduces an additional position-dependent coupling factor that increases exponentially along the length of the lattice. We will describe numerical and analytical frameworks for our model and show how it gives rise to a distinct mixture of localized edge states and bulk energy states.