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  • Letter
  • Open Access

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

Giuseppe De Tomasi1 and Ivan M. Khaymovich2,3

  • 1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
  • 2Nordita, Stockholm University and KTH Royal Institute of Technology, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden
  • 3Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia

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Phys. Rev. B 108, L180202 – Published 30 November, 2023

DOI: https://doi.org/10.1103/PhysRevB.108.L180202

Abstract

The power-law random banded matrix (PLRBM) is a paradigmatic ensemble to study the Anderson localization transition (AT). In d dimensions, the PLRBMs are random matrices with algebraic decaying off-diagonal elements Hnm∼1/|n−m|α, having AT at α=d. In this work, we investigate the fate of the PLRBM to non-Hermiticity (nH). 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 understand the model analytically by generalizing the Anderson-Levitov resonance counting technique to the nH case. We identify two competing mechanisms due to nH: favoring localization and 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, like in 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 and finds immediate application in phase transitions driven by weak measurements.

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Phys. Rev. B 108, L180202– Published 30 November, 2023
  • Received 10 March 2023
  • Revised 14 November 2023
  • Accepted 16 November 2023
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