Non-Hermitian tearing by dissipation

TL;DR

This paper introduces the concept of non-Hermitian tearing, a phase transition phenomenon in dissipative non-Hermitian systems, affecting bulk and boundary states, with applications to topological models.

Contribution

It proposes the theory of non-Hermitian tearing, describing phase transitions at exceptional points and analyzing their effects on topological models under dissipation.

Findings

Identification of imaginary line gap in energy bands.

Description of non-Hermitian tearing as a phase transition.

Application to topological models like SSH and Qi-Wu-Zhang.

Abstract

In the paper, we study the non-Hermitian system under dissipation and give the effective 2*2 Hamiltonian in the k-space by reducing the N*N Hamiltonian in the real space for them. It is discovered that the energy band shows an imaginary line gap. To describe these phenomena, we propose the theory of "non-Hermitian tearing", in which the tearability we define reveals a continuous phase transition at the exceptional point. The non-Hermitian tearing manifests in two forms -- separation of bulk state and decoupling of boundary state. In addition, we also explore the one-dimensional Su-Schrieffer-Heeger model and the Qi-Wu-Zhang model under dissipation using the theory of non-Hermitian tearing. Our results provide a theoretical approach for exploring the controlling of non-Hermitian physics on topological quantum states.