Single-particle excitations across the localization and many-body localization transition in quasi-periodic systems

Abstract

We study localization and many-body localization transition in one dimensional systems in the presence of deterministic quasi-periodic potential. We use single-particle excitations obtained through single-particle Green's function in real space to characterize the localization to delocalization transition. A single parameter scaling analysis of the ratio of the typical to average value of the local density of states (LDOS) of single particle excitations shows that the critical exponent with which the correlation length $\xi$ diverges at the transition point $\xi \sim |h-h_c{|}^{-\nu }$, coming from the localized side, satisfies the inequality $\nu \ge 1$ for the non-interacting Aubry-Andre (AA) model. For the interacting system with AA potential, we study single particle excitations produced in highly excited many-body eigenstates across the MBL transition and found that the critical exponent obtained from finite-size scaling of the ratio of the typical to average value of the LDOS satisfies $\nu \ge 1$ here as well. This analysis of local density of states shows that the localization and MBL transition in systems with quasi-periodic potential belong to a different universality class than the localization and MBL transition in systems with random disorder where $\nu \ge 2$. In complete contrast to this, finite-size scaling of the level spacing ratio is known to support the same universality class for MBL transitions in systems with quasiperiodic as well as random disorder potentials. For the interacting systems with quasiperiodic potentials, though finite-size scaling of the level spacing ratio shows a transition at $h_c^{lsr}$ which is close to the transition point obtained from LDOS within numerical precision, the critical exponent obtained from finite-size scaling of level spacing ratio is $\nu \sim 0.54$ in close similarity to the MBL systems with random disorder.

arXiv comment7 pages, 5 figures

References in corpus (40)

• Many body localization and thermalization in quantum statistical mechanics
• Many-body localization, thermalization, and entanglement
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Many-body localization: an introduction and selected topics
• Many-Body Localization in a Quasiperiodic System
• Coupling Identical 1D Many-Body Localized Systems
• Theory of the many-body localization transition in one dimensional systems
• Periodically Driving a Many-Body Localized Quantum System
• Universal properties of many-body delocalization transitions
• Signatures of Many-Body Localization in a Controlled Open Quantum System
• Avalanches and many-body resonances in many-body localized systems
• Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems
• Statistics and Scaling in Disordered Mesoscopic Electron Systems
• Two universality classes for the many-body localization transition
• Observation of many-body localization in a one-dimensional system with single-particle mobility edge
• Critical Properties of the Many-Body Localization Transition
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Many-body delocalization as a quantum avalanche
• A Measure of data-collapse for scaling
• Many body localization and quantum non-ergodicity in a model with a single-particle mobility edge
• Conductivity of disordered quantum lattice models at infinite temperature: Many-body localization
• Anderson localization and the quantum phase diagram of three dimensional disordered Dirac semimetals
• Many body localization in the presence of a single particle mobility edge
• Scaling Theory of Entanglement at the Many-Body Localization Transition
• Transport in quasiperiodic interacting systems: from superdiffusion to subdiffusion
• Level statistics across the many--body localization transition
• Correlated Fermions in a one-dimensional quasiperiodic potential
• Universal properties of many-body localization transitions in quasiperiodic systems
• Many-body delocalization dynamics in long Aubry-André quasiperiodic chains
• Butterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization
• Anomalous transport in the Aubry-André-Harper model in isolated and open systems
• Slow dynamics and strong finite-size effects in many-body localization with random and quasi-periodic potential
• Dynamical conductivity and its fluctuations along the crossover to many-body localization
• Many-Body Localization in Spin Chain Systems with Quasiperiodic Fields
• Local integrals of motion and the quasiperiodic many-body localization transition
• Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions
• Quantum criticality in the disordered Aubry-André model
• Multifractality at the Weyl semimetal-diffusive metal transition for generic disorder
• Transition between localized and extended states in the hierarchical Anderson model
• Initial State Dependent Dynamics Across Many-body Localization Transition

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