Recent theoretical and numerical evidence suggests that localization can survive in disordered many-body systems with very high energy density, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in extended quantum systems far from the zero-temperature limit. It separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting ("ergodic") phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present numerical evidence that many-body localization also occurs in models without disorder but rather a quasiperiodic potential. In one dimension, these systems already have a single-particle localization transition, and we show that this transition becomes a many-body localization transition upon the introduction of interactions. We also comment on possible relevance of our results to experimental studies of many-body dynamics of cold atoms and non-linear light in quasiperiodic potentials.

We study the zero temperature superfluid-insulator transition for a two-dimensional model of interacting, lattice bosons in the presence of quenched disorder and particle-hole symmetry. We follow the approach of a recent series of papers by Altman, Kafri, Polkovnikov, and Refael, in which the strong disorder renormalization group is used to study disordered bosons in one dimension. Adapting this method to two dimensions, we study several different species of disorder and uncover universal features of the superfluid-insulator transition. In particular, we locate an unstable finite disorder fixed point that governs the transition between the superfluid and a gapless, glassy insulator. We present numerical evidence that this glassy phase is the incompressible Mott glass and that the transition from this phase to the superfluid is driven by percolation-type process. Finally, we provide estimates of the critical exponents governing this transition.

A pair of recent Monte Carlo studies have reported evidence for and against a crossover from weak-to strongdisorder criticality in the one-dimensional dirty boson problem. The Monte Carlo analyses rely on measurement of two observables: the effective Luttinger parameter K eff and the superfluid susceptibility χ . The former quantity was previously calculated analytically, using the strong-disorder renormalization group (SDRG), by Altman, Kafri, Polkovnikov, and Refael. Here, we use an extension of the SDRG framework to find a nonuniversal anomalous dimension η sd characterizing the divergence of the susceptibility with system size, χ ∼ L 2−η sd . We show that η sd obeys the hyperscaling relation η sd = 1/2K eff . We also identify an important obstacle to measuring this exponent on finite-size systems and comment on the implications for numerics and experiments. Disordered bosonic systems pose theoretical challenges because of the unique pathologies of their noninteracting limits: At low temperatures, bosons condense into a localized single-particle state, forming a configuration that is intrinsically unstable to interactions. Therefore, Giamarchi and Schulz pioneered the study of the so-called "dirty boson problem" by perturbing a strongly interacting one-dimensional system with weak disorder. They identified a superfluidinsulator transition, belonging to the Kosterlitz-Thouless (KT) universality class, at which disorder is perturbatively irrelevant, 1 see also Refs. 2,3. It was long believed that this universality always characterizes the one-dimensional transition. In the past decade, the possibility has emerged that a novel criticality, also of KT type but with certain nonuniversal disorder-dependent features, takes over at sufficiently strongdisorder strength. This "strong-disorder criticality," first proposed by Altman, Kafri, Polkovnikov, and Refael, 4-6 remains unconfirmed.7 Recent Monte Carlo results by Hrahsheh and Vojta may provide evidence of the crossover between the two types of universality, 8 while calculations by Pielawa and Altman support the existence of a strong-disorder fixed point. 9 Meanwhile, experimental advances in various contexts, including cold atoms, spin systems, and dirty superconductors, have made it especially urgent to gain a better theoretical understanding of the seemingly universal properties of the dirty boson problem. [10][11][12][13][14][15] In this Rapid Communication, we extend the analysis of the universal aspects of the one-dimensional (1D) superfluidinsulator transition in the strong-disorder regime. In particular, we analytically calculate the superfluid susceptibility near the transition. This affords us a different perspective on recent numerical developments and allows us to clarify their relationship with the theoretical strong-disorder renormalization group (SDRG) framework. The model that we concentrate on is the particle-hole symmetric rotor modelThis model can describe a 1D array of superconducting islands connected by Josephson junctions, and we assume stron...

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