Many body localization and delocalization in the two dimensional continuum

Abstract

I discuss whether localization in the two dimensional continuum can be stable in the presence of short range interactions. I conclude that, for an impurity model of disorder, if the system is prepared below a critical temperature $T<T_c$, then perturbation theory about the localized phase converges almost everywhere. As a result, the system is at least asymptotically localized, and perhaps even truly many body localized, depending on how certain rare regions behave. Meanwhile, for $T>T_c$, perturbation theory fails to converge, which I interpret as interaction mediated delocalization. I calculate the boundary of the region of perturbative stability of localization in the interaction strength - temperature plane. I also discuss the behavior in a speckle disorder (relevant for cold atoms experiments) and conclude that perturbation theory about the non-interacting phase diverges for arbitrarily weak interactions with speckle disorder, suggesting that many body localization in the two dimensional continuum cannot survive away from the impurity limit.

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• Many body localization with long range interactions
• Dynamics and Transport at the Threshold of Many-Body Localization
• A many body localization proximity effect
• Localized systems coupled to small baths: from A${}_{nderson}$ to Z${}_{eno}$
• Eigenstate correlations around many-body localization transition
• A semi-classical limit for the many-body localization transition
• General theory of many body localized systems coupled to baths
• Spectral diffusion and scaling of many-body delocalization transitions
• Hilbert space shattering and dynamical freezing in the quantum Ising model
• Absence of many-body localization in a continuum
• Finite temperature disordered bosons in two dimensions
• Few-boson localization in a continuum with speckle disorder
• Localization of Extended Quantum Objects
• Many body localization proximity effects in platforms of coupled spins and bosons
• Symmetry breaking and localization in a random Schwinger model with commensuration
• Many-body localization in one dimensional optical lattice with speckle disorder
• Mobility edge of the two dimensional Bose-Hubbard model
• Many-body localization in continuum systems: two-dimensional bosons
• Mott glass from localization and confinement
• Many-body localization in Landau level subbands
• Observation of geometry dependent conductivity in two-dimensional electron systems
• Marginally localized edges of time-reversal symmetric topological superconductors
• Finite-size scaling analysis of localization transitions in the disordered two-dimensional Bose-Hubbard model within the fluctuation operator expansion method
• Localization and interactions in topological and non-topological bands in two dimensions
• Engineering many-body quantum Hamiltonians with non-ergodic properties using quantum Monte Carlo
• Critical localization with Van der Waals interactions
• AC Conductivity Crossover in Localized Superconductors