BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//6.4.7.2//EN TZID:Europe/Paris X-WR-TIMEZONE:Europe/Paris BEGIN:VEVENT UID:0-921@lptms.universite-paris-saclay.fr DTSTART;TZID=Europe/Paris:20240116T110000 DTEND;TZID=Europe/Paris:20240116T120000 DTSTAMP:20240108T214020Z URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm s-ivan-khaymovich-nordita/ SUMMARY:Séminaire du LPTMS : Ivan Khaymovich (Nordita Stockholm) - Salle d es séminaires du FAST et du LPTMS\, bâtiment Pascal n°530 - 16 Jan 24 1 1:00 DESCRIPTION:Localization enhancement in gain-loss non-Hermitian disordered modelsIvan Khaymovich (Nordita Stockholm)Recently the interest in non-Herm itian disordered models has been revived\, due to the claims of instabilit y of a many-body localization to a coupling to a bath. To describe such op en quantum systems\, one often focuses on an energy leakage to a bath\, us ing effective non-Hermitian Hamiltonians. A well-known Hatano-Nelson model [1]\, being a 1d Anderson localization (AL) model\, with different hoppin g amplitudes to the right/left\, shows AL breakdown\, as non-Hermiticity s uppresses the interference.Unlike this\, we consider models with the compl ex gain-loss disorder and show that in general these systems tend to the l ocalization due to non-Hermiticity. First\, we focus on a non-Hermitian ve rsion [2] of a Rosenzweig-Porter model [3]\, known to carry a fractal phas e [4] along with the AL and ergodic ones. We show that ergodic and localiz ed phases are stable against the non-Hermitian matrix entries\, while the fractal phase\, intact to non-Hermiticity of off-diagonal terms\, gives a way to AL in a gain-loss disorder. The understanding of this counterintuit ive phenomenon is given in terms of the cavity method and in addition in s imple hand-waving terms from the Fermi's golden rule\, applicable\, strict ly speaking\, to a Hermitian RP model. The main effect in this model is gi ven by the fact that the generally complex diagonal potential forms an eff ectively 2d (complex) distribution\, which parametrically increases the ba re level spacing and suppresses the resonances.Next\, we consider a power- law random banded matrix ensemble (PLRBM) [5]\, known to show AL transitio n (ALT) at the power of the power-law hopping decay a=d equal to the dimen sion d. In [6]\, we show that a non-Hermitian gain-loss disorder in PLRBM shifts ALT to smaller values $d/2<\;a_{AT}(W)<\;d$\, dependent on the disorder on-site W. A similar effect of the reduced critical disorder due to the gain-loss complex-valued disorder has been recently observed by us numerically [7]. In order to analytically explain the above numerical resu lts\, we derive an effective non-Hermitian resonance counting and show tha t 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 a re suppressed in the same way as in the non-Hermitian RP model.In the last part\, if time permits\, I will consider the effects of non-Hermitian dia gonal disorder on many-body localization in interacting systems and the lo calization in quantum random energy model [8] and show that the above para digm also works there.[1] N. Hatano\, D. R. Nelson\, "Localization Transit ions in Non-Hermitian Quantum Mechanics"\, PRL 77\, 570 (1996).[2] G. De T omasi\, I. M. K. "Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase"\, Phys. Rev. B\, 106\, 094204 (2022).[3] N. Rosenzweig and C. E. Porter\, “Repulsion of energy levels” in comp lex atomic spectra\,” Phys. Rev. B 120\, 1698 (1960).[4] V. E. Kravtsov\ , I. M. K.\, E. Cuevas\, and M. Amini\, “A random matrix model with loca lization and ergodic transitions\,” New J. Phys. 17\, 122002 (2015).[5] A. D. Mirlin\, Y. V. Fyodorov\, F.-M. Dittes\, J. Quezada\, and T. H. Seli gman\, “Transition from localized to extended eigenstates in the ensembl e of power-law random banded matrices\,” Phys. Rev. E 54\, 3221–3230 ( 1996).[6] G. De Tomasi\, I. M. K. "Non-Hermiticity induces localization: g ood and bad resonances in power-law random banded matrices"\, Phys. Rev. B 108\, L180202 (2023).[7] L. S. Levitov "Absence of localization of vibrat ional modes due to dipole-dipole interaction"\, EPL 9\, 83 (1989).[8] G. D e Tomasi\, I. M. K. "Stable many-body localization under random continuous measurements in the no-click limit"\, arXiv:2311.00019 . CATEGORIES:seminars LOCATION:Salle des séminaires du FAST et du LPTMS\, bâtiment Pascal n°53 0\, rue André Riviere\, Orsay\, 91405\, France X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=rue André Riviere\, Orsay\ , 91405\, France;X-APPLE-RADIUS=100;X-TITLE=Salle des séminaires du FAST et du LPTMS\, bâtiment Pascal n°530:geo:0,0 END:VEVENT BEGIN:VTIMEZONE TZID:Europe/Paris X-LIC-LOCATION:Europe/Paris BEGIN:STANDARD DTSTART:20231029T020000 TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET END:STANDARD END:VTIMEZONE END:VCALENDAR