on the May 19, 2025
Localization enhancement in gain-loss non-Hermitian disordered models
Abstract:
Recently the interest in non-Hermitian disordered models has been revived, due to the claims of instability of a many-body localization to a coupling to a bath.
To describe such open quantum systems, one often focuses on an energy leakage to a bath, using effective non-Hermitian Hamiltonians. A well-known Hatano-Nelson model [1], being a 1d Anderson localization (AL) model, with different hopping amplitudes to the right/left, shows AL breakdown, as non-Hermiticity suppresses the interference.
Unlike this, we consider models with the complex gain-loss disorder and show that in general these systems tend to the localization due to non-Hermiticity.
First, we consider a power-law random banded matrix ensemble (PLRBM) [2], known to show AL transition (ALT) at the power of the power-law hopping decay a=d equal to the dimension d. In [3], we show that a non-Hermitian gain-loss disorder in PLRBM shifts ALT to smaller values d/2<a<d, dependent on the on-site disorder amplitude .
A similar effect of the reduced critical disorder due to the gain-loss complex-valued disorder has been recently observed by us numerically [4].
In order to analytically explain the above numerical results, we derive an effective non-Hermitian resonance counting and show that the delocalization transition is driven by so-called "bad resonances", which cannot be removed by the wave-function hybridization (e.g., in the renormalization group approach), while the usual "Hermitian" resonances are suppressed.
In the last part, if time permits, I will consider the effects of non-Hermitian diagonal disorder on many-body localization in interacting systems and the localization in quantum random energy model [5] and show that the above paradigm also works there.
References
[1] N. Hatano, D. R. Nelson, "Localization Transitions in Non-Hermitian Quantum Mechanics", Phys. Rev. Lett. 77, 570 (1996).
[2] A. D. Mirlin, Y. V. Fyodorov, F.-M. Dittes, J. Quezada, and T. H. Seligman, “Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices", Phys. Rev. E 54, 3221–3230 (1996).
[3] G. De Tomasi, I. M. K. "Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices", Phys. Rev. B 108, L180202 (2023).
[4] L. S. Levitov "Absence of localization of vibrational modes due to dipole-dipole interaction", Europhys. Lett. 9, 83 (1989).
[5] G. De Tomasi, I. M. K. "Stable many-body localization under random continuous measurements in the no-click limit", Phys. Rev. B 109, 174205 (2024)
