Controlling energy spectra and skin effect via boundary conditions in non-Hermitian lattices

TL;DR

This paper investigates how boundary conditions influence spectral properties and the skin effect in non-Hermitian lattices, demonstrating control over eigenmode localization and spectral transitions through boundary tuning.

Contribution

It introduces a framework for controlling non-Hermitian spectral features via boundary conditions in lattice models, advancing understanding of boundary-induced phenomena.

Findings

Boundary conditions can be tuned to control the non-Hermitian skin effect.

Spectral transitions from real to complex are induced by boundary parameter adjustments.

The framework enables engineering of lattice models with desired spectral and localization properties.

Abstract

Non-Hermitian systems exhibit unique spectral properties, including the non-Hermitian skin effect and exceptional points, often influenced by boundary conditions. The modulation of these phenomena by generalized boundary conditions remains unexplored and not understood. Here, we analyze the Hatano-Nelson model with generalized boundary conditions induced by complex hopping amplitudes at the boundary. Using similarity transformations, we determine the conditions yielding real energy spectra and skin effect, and identify the emergence of exceptional points where spectra transition from real to complex. We demonstrate that tuning the boundary hopping amplitudes precisely controls the non-Hermitian skin effect, i.e., the localization of eigenmodes at the lattice edges. These findings reveal the sensitivity of spectral and localization properties to boundary conditions, providing a framework for engineering quantum lattice models with tailored spectral and localization features, with potential applications in quantum devices.