Criterion for the occurrence of many body localization in the presence of a single particle mobility edge

Abstract

Non-interacting fermions in one dimension can undergo a localization-delocalization transition in the presence of a quasi-periodic potential as a function of that potential. In the presence of interactions, this transition transforms into a Many-Body Localization (MBL) transition. Recent studies have suggested that this type of transition can also occur in models with quasi-periodic potentials that possess single particle mobility edges. Two such models were studied in PRL 115,230401(2015) but only one was found to exhibit an MBL transition in the presence of interactions while the other one did not. In this work we investigate the occurrence of MBL in the presence of weak interactions in five different models with single particle mobility edges in one dimension with a view to obtaining a criterion for the same. We find that not all such models undergo a thermal-MBL phase transition in presence of weak interactions. We propose a criterion to determine whether MBL is likely to occur in presence of interaction based only on the properties of the non-interacting models. The relevant quantity $\epsilon$ is a measure of how localized the localized states are relative to how delocalized the delocalized states are in the non-interacting model. We also study various other features of the non-interacting models such as the divergence of the localization length at the mobility edge and the presence or absence of `ergodicity' and localization in their many-body eigenstates. However, we find that these features cannot be used to predict the occurrence of MBL upon the introduction of weak interactions.

13 Pages, 15 Figures, accepted in Phys. Rev. B

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• Anomalous transport through algebraically localized states in one-dimension
• Many-body dynamics in long-range hopping model in the presence of correlated and uncorrelated disorder
• Transport in Stark Many Body Localized Systems
• Rational Approximations of Quasi-Periodic Problems via Projected Green's Functions
• Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations
• Signatures of multifractality in a periodically driven interacting Aubry-André model
• Transport in the non-ergodic extended phase of interacting quasiperiodic systems
• Many-body localized phase of bosonic dipoles in a tilted optical lattice
• Imbalance for a family of one-dimensional incommensurate models with mobility edges
• Many-body localized to ergodic transitions in a system with correlated disorder
• One-dimensional L{é}vy Quasicrystal
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Localization renormalization and quantum Hall systems
• Entanglement growth and information capacity in a quasiperiodic system with a single-particle mobility edge
• Probing quantum phase transition via quantum speed limit
• Subsystem localization in a two-leg ladder system
• Many-body critical phase in a quasiperiodic chain and dynamical Widom lines in Fock space properties
• Geometric quenches in quasi-disordered lattice system
• Many-body localization in a slowly varying potential
• Exact mobility edges in a slowly varying quasiperiodic ladder model