Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization

Autor: I. García-Mata, J. Martin, O. Giraud, B. Georgeot, R. Dubertrand, G. Lemarié
Přispěvatelé: Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), Consejo Nacional de Investigaciones Científicasy Tecnológicas, CONICET, Argentina, Institut de Physique Nucléaire, Atomique et de Spectroscopie, CESAM, Université de Liège, Bât. B15, B - 4000 Liège, Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche « Matière et interactions » (FeRMI), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, Physics and Electrical Engineering, Northumbria University, University of Northumbria at Newcastle [United Kingdom], MajuLab, National University of Singapore (NUS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Centre for Quantum Technologies [Singapore] (CQT), National University of Singapore (NUS), ANR-17-CE30-0024,COCOA,Contrôle de systèmes complexes d'atomes froids(2017), ANR-19-CE30-0013,GLADYS,De la nature vitreuse des systèmes quantiques désordonnés(2019), ANR-18-CE30-0017,MANYLOK,Localisation à N corps avec le Kicked Rotor(2018)
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Physical Review B
Physical Review B, 2022, 106, pp.214202. ⟨10.1103/PhysRevB.106.214202⟩
ISSN: 2469-9950
2469-9969
DOI: 10.1103/PhysRevB.106.214202⟩
Popis: The Anderson transition in random graphs has raised great interest, partly because of its analogy with the many-body localization (MBL) transition. Unlike the latter, many results for random graphs are now well established, in particular the existence and precise value of a critical disorder separating a localized from an ergodic delocalized phase. However, the renormalization group flow and the nature of the transition are not well understood. In turn, recent works on the MBL transition have made the remarkable prediction that the flow is of Kosterlitz-Thouless type. Here we show that the Anderson transition on graphs displays the same type of flow. Our work attests to the importance of rare branches along which wave functions have a much larger localization length $\xi_\parallel$ than the one in the transverse direction, $\xi_\perp$. Importantly, these two lengths have different critical behaviors: $\xi_\parallel$ diverges with a critical exponent $\nu_\parallel=1$, while $\xi_\perp$ reaches a finite universal value ${\xi_\perp^c}$ at the transition point $W_c$. Indeed, $\xi_\perp^{-1} \approx {\xi_\perp^c}^{-1} + \xi^{-1}$, with $\xi \sim (W-W_c)^{-\nu_\perp}$ associated with a new critical exponent $\nu_\perp = 1/2$, where $\exp( \xi)$ controls finite-size effects. The delocalized phase inherits the strongly non-ergodic properties of the critical regime at short scales, but is ergodic at large scales, with a unique critical exponent $\nu=1/2$. This shows a very strong analogy with the MBL transition: the behavior of $\xi_\perp$ is identical to that recently predicted for the typical localization length of MBL in a phenomenological renormalization group flow. We demonstrate these important properties for a smallworld complex network model and show the universality of our results by considering different network parameters and different key observables of Anderson localization.
Comment: 36 pages, 32 figures. Closest to the published version
Databáze: OpenAIRE
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