Topological Phases in a PT-Symmetric Dissipative Kitaev Chain

TL;DR

This paper explores topological phases in a dissipative Kitaev chain governed by a Lindblad equation, revealing PT symmetry and edge modes with zero eigenvalues, advancing understanding of open quantum systems.

Contribution

It introduces a classification of Lindbladians in terms of non-Hermitian topological phases and analyzes PT symmetry effects in dissipative topological systems.

Findings

Lindbladian retains PT symmetry, leading to common lifetime for bulk modes.

Edge modes emerge under open boundary conditions, with one having a zero eigenvalue.

Bulk modes can be characterized by non-Hermitian topological invariants.

Abstract

We study a topological phase in the dissipative Kitaev chain described by the Markovian quantum master equation. Based on the correspondence between Lindbladians, which generate the dissipative time-evolution, and non-Hermitian matrices, Lindbladians are classified in terms of non-Hermitian topological phases. We find out that the Lindbladian retains PT symmetry which is the prominent symmetry of open systems and then all the bulk modes can have a common lifetime. Moreover, when open boundary conditions are imposed on the system, the edge modes which break PT symmetry emerge, and one of the edge modes has a zero eigenvalue.