Transition from degeneracy to coalescence: theorem and applications

TL;DR

This paper establishes a theorem describing the transition from degeneracy points to exceptional points in Hermitian systems influenced by non-Hermitian effects, with applications to model systems and edge mode dynamics.

Contribution

It introduces a general theorem on the transition from degeneracy points to exceptional points in Hermitian systems with non-Hermitian terms, supported by exactly solvable models.

Findings

Transition between degeneracy and exceptional spectra driven by non-Hermitian tunnelings

Robustness of exceptional points to non-Hermitian term strength

Generation of coalescing edge modes in SSH-like models

Abstract

Exceptional point (EP) is exclusive for non-Hermitian system and distinct from that at a degeneracy point (DP), supporting intriguing dynamics, which can be utilized to probe quantum phase transition and prepare eigenstates in a Hermitian many-body system. In this work, we investigate the transition from DP for a Hermitian system to EP driven by non-Hermitian terms. We present a theorem on the existence of transition between DP and EP for a general system. The obtained EP is robust to the strength of non-Hermitian terms. We illustrate the theorem by an exactly solvable quasi-one-dimensional model, which allows the existence of transition between fully degeneracy and exceptional spectra driven by non-Hermitian tunnelings in real and k spaces, respectively. We also study the EP dynamics for generating coalescing edge modes in Su-Schrieffer-Heeger-like models. This finding reveals the ubiquitous connection between DP and EP.