Level statistics of extended states in random non-Hermitian Hamiltonians

Abstract

Absence of level repulsion between extended states in random non-Hermitian systems is demonstrated. As a result, the general Wigner-Dyson distributions of level spacing of diffusive metals in the usual Hermitian systems is replaced by the Poisson distribution for quasiparticle level spacing of non-Hermitian disordered metals in the thermodynamic limit of infinite system size. This is a very surprising result because Poisson statistics is universally true for the Anderson insulators where energy eigenstates do not overlap with each other so that energy levels are independent from each other. For disordered metals where different eigenstates overlap with each other, one should expect different levels trying to stay away from each other so that the Poisson distribution should not apply there. Our results show that the larger non-Hermitian energy (dissipation) can invalidate level repulsion principle that holds dearly in quantum mechanics. Thus, our theory provides a unified picture for recent discovery of so called "level attraction" in various systems. It provides also a theoretical basis for manipulating energy levels.arXiv:2003.02492v1 [cond-mat.mes-hall]

Non-Hermiticity-induced reentrant localization in a quasiperiodic lattice

“…where s i+1 = Re (E i+1 ) − Re (E i ) denotes the level spacing between the real part of the (i + 1)th and ith eigenenergies [49,56,57]. The average of r i which goes over all the eigenenergies gives rise to r = n r n /L.…”

“…These exotic phenomena bring potential applications including lasing [31][32][33], sensing [34][35][36][37][38], and topological light modulation [39][40][41]. Particularly, the interplay between disorder and non-Hermiticity has been recently explored [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. In non-Hermitian quasiperiodic lattice with asymmetric hopping or PT -symmetry, it is revealed that the non-Hermitian Anderson transition coincides with topological transition and complex-real energy transition [43][44][45][46].…”

Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems

“…Very recently, the study on disorder effect in non-Hermitian systems has also drawn extensive attentions [80][81][82][83][84][85][86][87][88][89][90][91][92][93]. Importantly, the NHSE could still exist in disordered samples [12][13][14][15][16][17] and leads to the breakdown of BBC for translational-symmetry-broken samples.…”

“…Although has achieved great successes in clean systems, the applicability of GBZ theory in disordered systems is still not fully understood because this theory is heavily based on the translational symmetry [52][53][54]. Therefore, the widely adopted GBZ theory may not be directly applicable [96] when disorder is presented [80][81][82][83][84][85][86][87][88][89][90][91][92][93][94][95]. The BBC mechanism as well as the quantitative description of the NHSE in disordered samples remain to be investigated.…”

Hermitian chiral boundary states in non-Hermitian topological insulators

“…Many theoretical and experimental works show that non-Hermicity gives rise to different phenomena that do not occur in a Hermitian system [50][51][52][53][54][55][56][57][58][59][60][61]. For instance, Poison distribution, universal level-spacing statistics of localized states in Hermitian systems, becomes quasi-particle level spacing statistics in metallic phases of non-Hermitian systems [62,63]. Moreover, a modified bulk-boundary correspondence is established to describe the non-Hermitian topological states of Su-Schrieffer-Heeger models [52,54,55], CIs [53,[64][65][66], and quantum spin Hall insulators [67].…”