Bosons refusing to thermalize in 2D Messy, interacting quantum-mechanical systems are difficult to analyze theoretically. In a single spatial dimension, the calculations are still tractable, and experiments have recently confirmed the prediction that sufficiently strong disorder can disrupt the transport of interacting particles. In two dimensions, however, the theoretical blueprint is missing. Choi et al. used single-site imaging of cold 87Rb atoms in an optical lattice to show that similar localization occurs in two-dimensional (2D) systems. The study highlights the power of quantum simulation to solve problems that are currently inaccessible to classical computing techniques. Science, this issue p. 1547 Single-site imaging in a two-dimensional optical lattice filled with interacting rubidium atoms shows that disorder can prevent thermalization. A fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept and challenged our understanding of the connection between statistical physics and quantum mechanics. Here we report on the observation of a many-body localization transition between thermal and localized phases for bosons in a two-dimensional disordered optical lattice. With our single-site–resolved measurements, we track the relaxation dynamics of an initially prepared out-of-equilibrium density pattern and find strong evidence for a diverging length scale when approaching the localization transition. Our experiments represent a demonstration and in-depth characterization of many-body localization in a regime not accessible with state-of-the-art simulations on classical computers.

Exploring the many-body localization transition in two dimensions

Localization properties of noninteracting quantum particles in one-dimensional incommensurate lattices are investigated with an exponential short-range hopping that is beyond the minimal nearest-neighbor tight-binding model. Energy dependent mobility edges are analytically predicted in this model and verified with numerical calculations. The results are then mapped to the continuum Schrödinger equation, and an approximate analytical expression for the localization phase diagram and the energy dependent mobility edges in the ground band is obtained.

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Predicted mobility edges in one-dimensional incommensurate optical lattices

Electronic transport in a one-dimensional mesoscopic ring threaded by a magnetic flux is studied in presence of Rashba and Dresselhaus spin-orbit interactions. A completely analytical technique within a tight-binding formalism unveils the spin-split bands in presence of the spin-orbit interactions and leads to a method of determining the strength of the Dresselhaus interaction. In addition to this, the persistent currents for ordered and disordered rings have been investigated numerically. It is observed that, the presence of the spin-orbit interaction, in general, leads to an enhanced amplitude of the persistent current. Numerical results corroborate the respective analytical findings.

Magneto-transport in a mesoscopic ring with Rashba and Dresselhaus spin-orbit interactions

The unrelated discoveries of quasicrystals and topological insulators have in turn challenged prevailing paradigms in condensed-matter physics. We find a surprising connection between quasicrystals and topological phases of matter: (i) quasicrystals exhibit nontrivial topological properties and (ii) these properties are attributed to dimensions higher than that of the quasicrystal. Specifically, we show, both theoretically and experimentally, that one-dimensional quasicrystals are assigned two-dimensional Chern numbers and, respectively, exhibit topologically protected boundary states equivalent to the edge states of a two-dimensional quantum Hall system. We harness the topological nature of these states to adiabatically pump light across the quasicrystal. We generalize our results to higher-dimensional systems and other topological indices. Hence, quasicrystals offer a new platform for the study of topological phases while their topology may better explain their surface properties.

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Topological States and Adiabatic Pumping in Quasicrystals

We propose an idea to investigate persistent current in individual arms of a multi-arm mesoscopic ring. Following a brief description of persistent current in a traditional mesoscopic ring pierced by an Aharonov-Bohm (AB) flux $\phi$, we examine the behavior of persistent currents in separate arms of a three-arm mesoscopic ring where upper and lower sub-rings are subject to AB fluxes $\phi_1$ and $\phi_2$, respectively. The present analysis may provide a basic framework to study magnetic response in individual branches of any complicated quantum network.

Distribution of Persistent Currents in a Multi-Arm Mesoscopic Ring: A Theoretical Study

A completely opposite behavior of electronic localization is revealed in a spatially non-uniform disordered material compared to the traditional spatially uniform disordered one. This fact is substantiated by considering an order-disorder separated (ODS) nanotube and studying the response of non-interacting electrons in presence of magnetic flux . We critically examine the behavior of flux induced energy spectra and circular current for different band fillings, and it is observed that maximum current amplitude (MCA) gradually decreases with disorder strength for weak disorder regime, while surprisingly it (MCA) increases in the limit of strong disorder suppressing the effect of disorder, resulting higher conductivity . This is further confirmed by investigating Drude weight and exactly same anomalous feature is noticed. It clearly gives a hint that localization-to-delocalization transition (LTD) is expected upon the variation of disorder strength which is justified by analyzing the nature of different eigenstates. Our analysis may give some significant inputs in analyzing conducting properties of different doped materials.

Madhuparna Banerjee

Papers

Unconventional localization phenomena in a spatially non-uniform disordered material

Magnetotransport in fractal network with loop sub-structures: Anisotropic effect and delocalization