Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect

TL;DR

This paper provides exact solutions for non-Hermitian systems with generalized boundary conditions, revealing the size-dependent boundary effects and the fragile nature of the skin effect, which is sensitive to boundary perturbations and lattice size.

Contribution

It introduces exact solutions for non-Hermitian models with generalized boundaries, uncovering the boundary sensitivity and the conditions for skin effect survival.

Findings

Skin effect exists when one boundary hopping term vanishes.

Skin effect is fragile under tiny boundary perturbations in the thermodynamic limit.

New phase diagram for the non-Hermitian SSH model on the boundary critical line.

Abstract

Systems with non-Hermitian skin effects are very sensitive to the imposed boundary conditions and lattice size, and thus an important question is whether non-Hermitian skin effects can survive when deviating from the open boundary condition. To unveil the origin of boundary sensitivity, we present exact solutions for one-dimensional non-Hermitian models with generalized boundary conditions and study rigorously the interplay effect of lattice size and boundary terms. Besides the open boundary condition, we identify the existence of non-Hermitian skin effect when one of the boundary hopping terms vanishes. Apart from this critical line on the boundary parameter space, we find that the skin effect is fragile under any tiny boundary perturbation in the thermodynamic limit, although it can survive in a finite size system. Moreover, we demonstrate that the non-Hermitian Su-Schreieffer-Heeger model exhibits a new phase diagram in the boundary critical line, which is different from either open or periodical boundary case.