Beyond characteristic equations: A unified one-dimensional non-Bloch band theory via wavefunction data

TL;DR

This paper introduces a unified one-dimensional non-Bloch band theory that incorporates wavefunction data to accurately determine spectra in non-Hermitian systems with symmetries, surpassing traditional characteristic equation methods.

Contribution

It develops a new framework that includes wavefunction information to address limitations of existing non-Bloch band theory in symmetric non-Hermitian systems.

Findings

Accurately captures energy spectra and signal responses in symmetric systems.

Identifies the role of wavefunction data and symmetry in non-Hermitian band theory.

Resolves ambiguities where characteristic equations alone are insufficient.

Abstract

Non-Hermitian systems play a central role in nonequilibrium physics, where determining the energy spectrum under open boundary conditions is a fundamental problem. Non-Bloch band theory, based on the characteristic equation $\text{det}[E - H(\beta)] = 0$, has emerged as a key tool for this task. However, we show that this framework becomes insufficient in systems with certain symmetries, where identical characteristic equations can yield different spectra. To resolve this, we develop a unified theory that incorporates additional wavefunction information beyond the characteristic equation. Our framework accurately captures spectral properties such as the energy spectrum and the end-to-end signal response in a broad class of systems, particularly those with high symmetry. It reveals the essential role of wavefunction information and symmetry in shaping non-Hermitian band theory.