Ideal quantum glass transitions: many-body localization without quenched disorder?

In this work the role of disorder, interaction and temperature in the physics of quantum non-ergodic systems is discussed. I first review what is meant by thermalization in closed quantum systems, and how ergodicity is violated in the presence of strong disorder, due to the phenomenon of Anderson localization. I explain why localization can be stable against the addition of weak dephasing interactions, and how this leads to the very rich phenomenology associated with many-body localization. I also briefly compare localized systems with their closest classical analogue, which are glasses, and discuss their similarities and differences, the most striking being that in quantum systems genuine non ergodicity can be proven in some cases, while in classical systems it is a matter of debate whether thermalization eventually takes place at very long times. Up to now, many-body localization has been studies in the region of strong disorder and weak interaction. I show that strongly interacting systems display phenomena very similar to localization, even in the absence of disorder. In such systems, dynamics starting from a random inhomogeneous initial condition are non-perturbatively slow, and relaxation takes place only in exponentially long times. While in the thermodynamic limit ergodicity is ultimately restored due to rare events, from the practical point of view such systems look as localized on their initial condition, and this behavior can be studied experimentally. Since their behavior shares similarities with both many-body localized and classical glassy systems, these models are termed \u201cquantum glasses\u201d. Apart from the interplay between disorder and interaction, another important issue concerns the role of temperature for the physics of localization. In non-interacting systems, an energy threshold separating delocalized and localized states exist, termed \u201cmobility edge\u201d. It is commonly believed that a mobility edge should exist in interacting systems, too. I argue that this scenario is inconsistent because inclusions of the ergodic phase in the supposedly localized phase can serve as mobile baths that induce global delocalization. I conclude that true non-ergodicity can be present only if the whole spectrum is localized. Therefore, the putative transition as a function of temperature is reduced to a sharp crossover. I numerically show that the previously reported mobility edges can not be distinguished from finite size effects. Finally, the relevance of my results for realistic experimental situations is discussed

Absence of many-body mobility edges

Localization transitions as a function of temperature require a many-body mobility edge in energy, separating localized from ergodic states. We argue that this scenario is inconsistent because local fluctuations into the ergodic phase within the supposedly localized phase can serve as mobile bubbles that induce global delocalization. Such fluctuations inevitably appear with a low but finite density anywhere in any typical state. We conclude that the only possibility for many-body localization to occur are lattice models that are localized at all energies. Building on a close analogy with a model of assisted two-particle hopping, where interactions induce delocalization, we argue why hot bubbles are mobile and do not localize upon diluting their energy. Numerical tests of our scenario show that previously reported mobility edges cannot be distinguished from finite-size effects.Comment: 16 pages, 6 figure

Self-averaging in many-body quantum systems out of equilibrium. II. Approach to the localized phase

The self-averaging behavior of interacting many-body quantum systems has been mostly studied at equilibrium. The present work addresses what happens out of equilibrium, as the increase of the strength of onsite disorder takes the system to the localized phase. We consider two local and two non-local quantities of great experimental and theoretical interest. In the delocalized phase, self-averaging depends on the observable and on the time scale, but the picture simplifies substantially when localization is reached. In the localized phase, the local observables become self-averaging at all times, while the non-local quantities are throughout non-self-averaging. These behaviors are explained and scaling analysis are provided using the $\ell$-bits model and a toy model.Comment: 14 pages, 7 figures; new title, new section, scaling analysis and analytical result

Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems

Despite its importance to experiments, numerical simulations, and the development of theoretical models, self-averaging in many-body quantum systems out of equilibrium remains underinvestigated. Usually, in the chaotic regime, self-averaging is taken for granted. The numerical and analytical results presented here force us to rethink these expectations. They demonstrate that self-averaging properties depend on the quantity and also on the time scale considered. We show analytically that the survival probability in chaotic systems is not self-averaging at any time scale, even when evolved under full random matrices.We also analyze the participation ratio, Rényi entropies, the spin autocorrelation function from experiments with cold atoms, and the connected spin-spin correlation function from experiments with ion traps. We find that self-averaging holds at short times for the quantities that are local in space, while at long times, self-averaging applies for quantities that are local in time. Various behaviors are revealed at intermediate time scales

Absence of many-body mobility edges

© 2016 American Physical Society. Localization transitions as a function of temperature require a many-body mobility edge in energy, separating localized from ergodic states. We argue that this scenario is inconsistent because local fluctuations into the ergodic phase within the supposedly localized phase can serve as mobile bubbles that induce global delocalization. Such fluctuations inevitably appear with a low but finite density anywhere in any typical state. We conclude that the only possibility for many-body localization to occur is lattice models that are localized at all energies. Building on a close analogy with a model of assisted two-particle hopping, where interactions induce delocalization, we argue why hot bubbles are mobile and do not localize upon diluting their energy. Numerical tests of our scenario show that previously reported mobility edges cannot be distinguished from finite-size effects.16 pages, 6 figuresstatus: publishe

Dynamics in many-body localized quantum systems without disorder

We study the relaxation dynamics of strongly interacting quantum systems that display a kind of many-body localization in spite of their translation-invariant Hamiltonian. We show that dynamics starting from a random initial configuration is nonperturbatively slow in the hopping strength, and potentially genuinely nonergodic in the thermodynamic limit. In finite systems with periodic boundary conditions, density relaxation takes place in two stages, which are separated by a long out-of-equilibrium plateau whose duration diverges exponentially with the system size. We estimate the phase boundary of this quantum glass phase, and discuss the role of local resonan