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Register a new userMatter Wave Transport and Anderson Localization in Anisotropic 3D Disorder
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Authors
Marie Piraud
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We study quantum transport in anisotropic 3D disorder and show that non rotation invariant correlations can induce rich diffusion and localization properties. For instance, structured finite-range correlations can lead to the inversion of the transport anisotropy. Moreover, working beyond the self-consistent theory of localization, we include the disorder-induced shift of the energy states and show that it strongly affects the mobility edge. Implications to recent experiments are discussed.
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Many-body localization (MBL) is an example of a dynamical phase of matter that avoids thermalization. While the MBL phase is robust to weak local perturbations, the fate of an MBL system coupled to a thermalizing quantum system that represents a heat bath is an open question that is actively investigated theoretically and experimentally. In this work we consider the stability of an Anderson insulator with a finite density of particles interacting with a single mobile impurity -- a small quantum bath. We give perturbative arguments that support the stability of localization in the strong interaction regime. Large scale tensor network simulations of dynamics are employed to corroborate the presence of the localized phase and give quantitative predictions in the thermodynamic limit. We develop a phenomenological description of the dynamics in the strong interaction regime, and demonstrate that the impurity effectively turns the Anderson insulator into an MBL phase, giving rise to non-trivial entanglement dynamics well captured by our phenomenology.
We evaluate the localization length of the wave (or Schroedinger) equation in the presence of a disordered speckle potential. This is relevant for experiments on cold atoms in optical speckle potentials. We focus on the limit of large disorder, where the Born approximation breaks down and derive an expression valid in the quasi-metallic phase at large disorder. This phase becomes strongly localized and the effective mobility edge disappears.
Many-body localized (MBL) systems do not approach thermal equilibrium under their intrinsic dynamics; MBL and conventional thermalizing systems form distinct dynamical phases of matter, separated by a phase transition at which equilibrium statistical mechanics breaks down. True MBL is known to occur only under certain stringent conditions for perfectly isolated one-dimensional systems, with Hamiltonians that have strictly short-range interactions and lack any continuous non-Abelian symmetries. However, in practice, even systems that are not strictly MBL can be nearly MBL, with equilibration rates that are far slower than their other intrinsic timescales; thus, anomalously slow relaxation occurs in a much broader class of systems than strict MBL. In this review we address transport and dynamics in such nearly-MBL systems from a unified perspective. Our discussion covers various classes of such systems: (i) disordered and quasiperiodic systems on the thermal side of the MBL-thermal transition; (ii) systems that are strongly disordered, but obstructed from localizing because of symmetry, interaction range, or dimensionality; (iii) multiple-component systems, in which some components would in isolation be MBL but others are not; and finally (iv) driven systems whose dynamics lead to exponentially slow rates of heating to infinite temperature. A theme common to many of these problems is that they can be understood in terms of approximately localized degrees of freedom coupled to a heat bath (or baths) consisting of thermal degrees of freedom; however, this putative bath is itself nontrivial, being either small or very slowly relaxing. We discuss anomalous transport, diverging relaxation times, and other signatures of the proximity to MBL in these systems. We also survey recent theoretical and numerical methods that have been applied to study dynamics on either side of the MBL transition.
The understanding of disordered quantum systems is still far from being complete, despite many decades of research on a variety of physical systems. In this review we discuss how Bose-Einstein condensates of ultracold atoms in disordered potentials have opened a new window for studying fundamental phenomena related to disorder. In particular, we point our attention to recent experimental studies on Anderson localization and on the interplay of disorder and weak interactions. These realize a very promising starting point for a deeper understanding of the complex behaviour of interacting, disordered systems.
Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable long-range orders forbidden in equilibrium. Specifically, we show that the interplay of symmetry breaking and localization in the quasiperiodic quantum Ising chain produces a emph{quasiperiodic Ising glass} stable at all energy densities. The glass order parameter vanishes with an essential singularity at the melting transition with no signatures in the equilibrium properties. The zero temperature phase diagram is also surprisingly rich, consisting of paramagnetic, ferromagnetic and quasiperiodically alternating ground state phases with extended, localized and critically delocalized low energy excitations. The system exhibits an unusual quantum Ising transition whose properties are intermediate between those of the clean and infinite randomness Ising transitions. Many of these results follow from a geometric generalization of the Aubry-Andre duality which we develop. The quasiperiodic Ising glass may be realized in near term quantum optical experiments.
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