{"id":11322,"date":"2025-01-02T11:34:55","date_gmt":"2025-01-02T10:34:55","guid":{"rendered":"https:\/\/fermi.univ-tlse3.fr\/?post_type=tribe_events&p=11322"},"modified":"2025-01-02T11:36:05","modified_gmt":"2025-01-02T10:36:05","slug":"localization-enhancement-in-gain-loss-non-hermitian-disordered-models-ivan-khaymovich-lpt-seminar-07-01-2025-14h","status":"publish","type":"tribe_events","link":"https:\/\/fermi.univ-tlse3.fr\/fr\/home\/event\/localization-enhancement-in-gain-loss-non-hermitian-disordered-models-ivan-khaymovich-lpt-seminar-07-01-2025-14h\/","title":{"rendered":"Localization enhancement in gain-loss non-Hermitian disordered models. – (Ivan Khaymovich \/ LPT \/ Seminar). – 07\/01\/2025, 14H"},"content":{"rendered":"

S\u00e9minaire LPT<\/span><\/p>\n

Ivan Khaymovich <\/strong><\/span>(Nordita, Stockholm)<\/span><\/p>\n

Seminar LPT, 07\/01\/2025, 14H, 3R4, salle de conf\u00e9rence<\/span><\/p>\n

Summary<\/strong><\/span><\/p>\n

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.
\nTo 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]<\/strong>, being a 1d Anderson localization (AL) model, with different hopping amplitudes to the right\/left, shows AL breakdown, as non-Hermiticity suppresses the interference.<\/p>\n

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.<\/p>\n

First, we consider a power-law random banded matrix ensemble (PLRBM) [2]<\/strong>, known to show AL transition (ALT) at the power of the power-law hopping decay a=d equal to the dimension d. In [3]<\/strong>, we show that a non-Hermitian gain-loss disorder in PLRBM shifts ALT to smaller values d\/2<\/p>\n

A similar effect of the reduced critical disorder due to the gain-loss complex-valued disorder has been recently observed by us numerically [4]<\/strong>. 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 \u00ab\u00a0bad resonances\u00a0\u00bb, which cannot be removed by the wave-function hybridization (e.g., in the renormalization group approach), while the usual \u00ab\u00a0Hermitian\u00a0\u00bb 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]<\/strong> and show that the above paradigm also works there.<\/p>\n

References<\/strong><\/p>\n

[1]<\/strong> N. Hatano, D. R. Nelson, \u00ab\u00a0Localization Transitions in Non-Hermitian Quantum Mechanics\u00a0\u00bb, Phys. Rev. Lett. 77, 570 (1996)<\/a><\/a>.<\/p>\n

[2]<\/strong> A. D. Mirlin, Y. V. Fyodorov, F.-M.\u00a0Dittes, J. Quezada, and T. H. Seligman, \u00ab\u00a0Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices\u00a0\u00bb, Phys. Rev. E 54, 3221\u20133230 (1996)<\/a><\/a>.<\/p>\n

[3]<\/strong> G. De Tomasi, I. M.\u00a0K. \u00ab\u00a0Non-Hermiticity induces localization\u00a0: good and bad resonances in power-law random banded matrices\u00a0\u00bb, Phys. Rev. B 108, L180202 (2023)<\/a><\/a>.
\n
\n[4]<\/strong> L. S. Levitov \u00ab\u00a0Absence of localization of vibrational modes due to dipole-dipole interaction\u00a0\u00bb, Europhys. Lett. 9, 83 (1989).<\/p>\n

[5]<\/strong> G. De Tomasi, I. M.\u00a0K. \u00ab\u00a0Stable many-body localization under random continuous measurements in the no-click limit\u00a0\u00bb, Phys. Rev. B 109, 174205 (2024)<\/a><\/a>.<\/p>\n

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