G. De Tomasi, I. M. Khaymovich, “Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices”, G. De Tomasi, I. M. Khaymovich (2023)


The power-law random banded matrix (PLRBM) is a paradigmatic ensemble to study the Anderson localization transition (AT). In d-dimension the PLRBM are random matrices with algebraic decaying off-diagonal elements Hn⃗ m⃗ ∼1/|n⃗ −m⃗ |α, having AT at α=d. In this work, we investigate the fate of the PLRBM to non-Hermiticity. We consider the case where the random on-site diagonal potential takes complex values, mimicking an open system, subject to random gain-loss terms. We provide an analytical understanding of the model by generalizing the Anderson-Levitov resonance counting technique to the non-Hermitian case. This generalization identifies two competing mechanisms due to non-Hermiticity: one favoring localization and the other delocalization. The competition between the two gives rise to AT at d/2≤α≤d. The value of the critical α depends on the strength of the on-site potential, reminiscent of Hermitian disordered short-range models in d>2. Within the localized phase, the wave functions are algebraically localized with an exponent α even for α<d. This result provides an example of non-Hermiticity-induced localization.


Physical Review B