Bulk-boundary correspondence in disordered non-Hermitian systems

Zhi-Qiang Zhang; Hongfang Liu; Haiwen Liu; Hua Jiang; X C Xie

doi:10.1016/j.scib.2023.01.002

Bulk-boundary correspondence in disordered non-Hermitian systems

Sci Bull (Beijing). 2023 Jan 30;68(2):157-164. doi: 10.1016/j.scib.2023.01.002. Epub 2023 Jan 6.

Authors

Zhi-Qiang Zhang¹, Hongfang Liu¹, Haiwen Liu², Hua Jiang³, X C Xie⁴

Affiliations

¹ School of Physical Science and Technology, Soochow University, Suzhou 215006, China; Institute for Advanced Study, Soochow University, Suzhou 215006, China.
² Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China.
³ School of Physical Science and Technology, Soochow University, Suzhou 215006, China; Institute for Advanced Study, Soochow University, Suzhou 215006, China. Electronic address: jianghuaphy@suda.edu.cn.
⁴ International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China.

PMID: 36653216
DOI: 10.1016/j.scib.2023.01.002

Abstract

The bulk-boundary correspondence (BBC) refers to the consistency between eigenvalues calculated under open and periodic boundary conditions. This consistency can be destroyed in systems with non-Hermitian skin effect (NHSE). In spite of the great success of the generalized Brillouin zone (GBZ) theory in clean non-Hermitian systems, the applicability of GBZ theory is questionable when the translational symmetry is broken. Thus, it is of great value to rebuild the BBC for disordered samples, which extends the application of GBZ theory in non-Hermitian systems. Here, we propose a scheme to reconstruct BBC, which can be regarded as the solution of an optimization problem. By solving the optimization problem analytically, we reconstruct the BBC and obtain the modified GBZ theory in several prototypical disordered non-Hermitian models. The modified GBZ theory provides a precise description of the fantastic NHSE, which predicts the asynchronous-disorder-reversed NHSE's directions.

Keywords: Bulk-boundary correspondence; Disorder effect; Generalized Brillouin zone; Non-Hermitian skin effect.