Non-Bloch band theory in bosonic Bogoliubov-de Gennes systems

TL;DR

This paper develops a non-Bloch band theory for bosonic BdG systems, enabling analysis of non-Hermitian effects like the skin effect and instabilities in open boundary conditions.

Contribution

It introduces a method to calculate the generalized Brillouin zone and energy spectrum in bosonic BdG systems with open boundaries, revealing non-Hermitian phenomena.

Findings

Bosonic Kitaev-Majorana chain shows non-Hermitian skin effect.

Reentrant behavior and instability are observed.

The theory is a powerful tool for non-Hermitian analysis in bosonic systems.

Abstract

In recent research, it has been shown that non-Hermitian systems exhibit sensitivity to boundaries, and it is caused by the non-Hermitian skin effect. In this work, we construct the non-Bloch band theory in bosonic Bogoliubov--de Gennes (BdG) systems. From our theory, we can calculate the generalized Brillouin zone and the energy spectrum in such systems with open boundary conditions in the thermodynamic limit, and we can thus discuss its non-Hermitian nature, despite Hermiticity of an original Hamiltonian. In fact, we find that the bosonic Kitaev-Majorana chain exhibits rich aspects of the non-Hermitian skin effect, such as instability against infinitesimal perturbations and reentrant behavior, in terms of the non-Bloch band theory. This result indicates that our theory is powerful tool for studying non-Hermitian nature in bosonic BdG systems.