Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems

Abstract

The consistency between eigenvalues calculated under open and periodic boundary conditions, named as bulk-bulk correspondence (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 BBC for disorder samples, which extends the application of GBZ theory in non-Hermitian systems. Here, we propose a scheme reconstructing BBC, which can be regarded as the solution of an optimization problem. By solving this optimization problem analytically, we reconstruct the 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.

Non-Hermitian topological phases: principles and prospects

“…Disorder, being ubiquitous in nature, has gained a lot of interest [189,207,[230][231][232], including in the context of non-Hermitian settings. The interplay of disorder and non-Hermiticity has led to the discovery of several new physical phenomena, some entirely unique to non-Hermitian systems [170,[232][233][234][235][236]. The study of disorder leads to the requirement of quantities which are 'self-averaging' under disorder, i.e.…”

Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices

“…Such a phenomenon is called non-Hermitian skin effect (NHSE) and has a significant effect on the systems' properties [43][44][45][46][47][48][49][50][51][52][53][54][55]. For instance, the conventional principle of bulk-boundary correspondence * zengqibo@cnu.edu.cn (BBC) of topological phases in Hermitian system breaks down in nonreciprocal systems due to the NHSE, which has motivated several new methods to recover the BBC in non-Hermitian topological systems [44,45,[56][57][58][59][60][61][62]. The nonreciprocity can also induce delocalization effects in the Anderson localization phase transition [32,[63][64][65][66][67][68].…”

Real non-Hermitian energy spectra without any symmetry

“…Non-Hermitian systems have recently inspired intense research efforts for their unconventional mathematical properties and physical robustness, such as enlarged topological symmetries, [1][2][3][4][5][6][7][8] exceptional point sensing, [9][10][11][12][13][14][15] quantized classical responses, [16] modified bulk-boundary correspondences, [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] unconventional entanglement entropy scaling, [4,[33][34][35][36][37][38][39] enhanced Rabi oscillations, [26,40,41] and effective non-Hermitian curved space. [42,43] Yet, many of these exciting phenomena are often difficult to probe experimentally due to their intrinsically unstable nature from complex eigenenergies.…”