Bulk-boundary correspondence in disordered non-Hermitian systems

• DOI: 10.1016/j.scib.2023.01.002
• Publication Date: 2023-01-06T02:03:51Z
• Authors: Zhi-Qiang Zhang; Hongfang Liu; Haiwen Liu; Hua Jiang; X.C. Xie
• Keywords: 0103 physical sciences; FOS: Physical sciences; Disordered Systems and Neural Networks (cond-mat.dis-nn); Condensed Matter - Disordered Systems and Neural Networks; 01 natural sciences

The consistency between eigenvalues calculated under open and periodic boundary conditions, named as {\it bulk-bulk correspondence} ($\mathcal{BBC}$), 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 $\mathcal{BBC}$ for disorder samples, which extends the application of GBZ theory in non-Hermitian systems. Here, we propose a scheme reconstructing $\mathcal{BBC}$, which can be regarded as the solution of an optimization problem. By solving this optimization problem analytically, we reconstruct the $\mathcal{BBC}$ and obtain the modified GBZ theory in several prototypical disordered non-Hermitian models. The modified GBZ theory gives a precise description of NHSE, which predicts the intriguing disorder-enhanced and disorder-irrelevant NHSEs.<br/>5 pages, 3 figures, including Supplementary Materials<br/>