Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices

• URL: http://arxiv.org/abs/2302.00015v2
• Date: Thu, 2 Nov 2023 09:02:47 GMT
• Title: Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices
• Authors: Giuseppe De Tomasi and Ivan M. Khaymovich
• Abstract summary: We study the fate of the power-law random banded matrix (PLRBM) to non-Hermiticity. The value of the critical $alpha$ depends on the strength of the on-site potential. This result provides an example of non-Hermiticity-induced localization.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $H_{\vec{n}\vec{m}}\sim 1/|\vec{n}-\vec{m}|^\alpha$, having AT at $\alpha=d$. 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 $d/2\le \alpha\le d$. The value of the critical $\alpha$ 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 $\alpha$ even for $\alpha<d$. This result provides an example of non-Hermiticity-induced localization.

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