A toy model for anomalous transport and Griffiths effects near the Many-Body Localization transition

Abstract

We introduce and study a toy model for anomalous transport and Griffiths effects in one dimensional quantum disordered isolated systems near the Many-Body Localization (MBL) transitions. The model is constituted by a collection of 1d tight-binding chains with on-site random energies, locally coupled to a weak GOE-like perturbation, which mimics the effect of thermal inclusions due to delocalizing interactions by providing a local broadening of the Poisson spectrum. While in absence of such a coupling the model is localized as expected for the one dimensional Anderson model, increasing the coupling with the GOE perturbation we find a delocalization transition to a conducting one driven by the proliferation of quantum avalanches which does not fit the standard paradigm of Anderson localization. In particular an intermediate Griffiths region emerges, where exponentially distributed insulating segments coexist with a few, rare resonances. Typical correlations decay exponentially fast, while average correlations decay as stretched exponential and diverge with the length of the chain, indicating that the conducting inclusions have a fractal structure and that the localization length is broadly distributed at the critical point. This behavior is consistent with a Kosterlitz-Thouless-like criticality of the transition. Transport and relaxation are dominated by rare resonances and rare strong insulating regions, and show anomalous behaviors strikingly similar to those observed in recent simulations and experiments in the bad metal delocalized phase preceding MBL. In particular, we find sub-diffusive transport and power-laws decay of the return probability at large times, with exponents that gradually change as one moves across the intermediate region. Concomitantly, the a.c. conductivity vanishes near zero frequency with an anomalous power-law.

20 pages, 15 figures

References in corpus (16)

• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Localization of interacting fermions at high temperature
• Phenomenology of fully many-body-localized systems
• Integrals of motion in the Many-Body localized phase
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Recent progress in many-body localization
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Anomalous thermalization in ergodic systems
• How a small quantum bath can thermalize long localized chains
• Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
• Non-ergodic phases in strongly disordered random regular graphs
• Delocalized Glassy Dynamics and Many Body Localization
• Renormalization-group study of the many-body localization transition in one dimension
• Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
• Localized systems coupled to small baths: from A${}_{nderson}$ to Z${}_{eno}$

Cited by in corpus (10)

• Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain
• Subdiffusion in a 1D Anderson insulator with random dephasing: Finite-size scaling, Griffiths effects, and possible implications for many-body localization
• Local Integrals of Motion in Quasiperiodic Many-Body Localized Systems
• Interaction-Driven Instabilities in the Random-Field XXZ Chain
• Destruction of Localization by Thermal Inclusions: Anomalous Transport and Griffiths Effects in the Anderson and André-Aubry-Harper Models
• Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
• The connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains
• Characterizing the many-body localization transition through correlations
• Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder
• Multifractality in high-dimensional graphs induced by correlated radial disorder