We consider the many-body localization-delocalization transition for strongly interacting one- dimensional disordered bosons and construct the full picture of finite temperature behavior of this system. This picture shows two insulator-fluid transiti
ons at any finite temperature when varying the interaction strength. At weak interactions an increase in the interaction strength leads to insulator->fluid transition, and for large interactions one has a reentrance to the insulator regime.
Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal dimensions $f(al
pha)$ defined in Eq.(3), remains positive for $alpha$ noticeably far from 1 even when the disorder is several times weaker than the one which leads to the Anderson localization, i.e. the ergodicity can be reached only in the absence of disorder. The one-particle multifractality on the Bethe lattice signals on a possible inapplicability of the equipartition law to a generic many-body quantum system as long as it remains isolated.
We consider weakly interacting bosons in a 1D quasiperiodic potential (Aubry-Azbel-Harper model) in the regime where all single-particle states are localized. We show that the interparticle interaction may lead to the many-body delocalization and we
obtain the finite-temperature phase diagram. Counterintuitively, in a wide range of parameters the delocalization requires stronger cou- pling as the temperature increases. This means that the system of bosons can undergo a transition from a fluid to insulator (glass) state under heating.
We consider chiral electrons moving along the 1D helical edge of a 2D topological insulator and interacting with a disordered chain of Kondo impurities. Assuming the electron-spin couplings of random anisotropies, we map this system to the problem of
the pinning of the charge density wave by the disordered potential. This mapping proves that arbitrary weak anisotropic disorder in coupling of chiral electrons with spin impurities leads to the Anderson localization of the edge states.
We discuss quantum propagation of dipole excitations in two dimensions. This problem differs from the conventional Anderson localization due to existence of long range hops. We found that the critical wavefunctions of the dipoles always exist which m
anifest themselves by a scale independent diffusion constant. If the system is T-invariant the states are critical for all values of the parameters. Otherwise, there can be a metal-insulator transition between this ordinary diffusion and the Levy-flights (the diffusion constant logarithmically increasing with the scale). These results follow from the two-loop analysis of the modified non-linear supermatrix $sigma$-model.
The superconductor-insulator transition (SIT) in regular arrays of Josephson junctions is studied at low temperatures. Near the transition a Ginzburg-Landau type action containing the imaginary time is derived. The new feature of this action is that
it contains a gauge field $Phi $ describing the Coulomb interaction and changing the standard critical behavior. The solution of renormalization group (RG) equations derived at zero temperature $T=0$ in the space dimensionality $d=3$ shows that the SIT is always of the first order. At finite temperatures, a tricritical point separates the lines of the first and second order phase transitions. The same conclusion holds for $d=2$ if the mutual capacitance is larger than the distance between junctions.
It is commonly accepted that there are no phase transitions in one-dimensional (1D) systems at a finite temperature, because long-range correlations are destroyed by thermal fluctuations. Here we demonstrate that the 1D gas of short-range interacting
bosons in the presence of disorder can undergo a finite temperature phase transition between two distinct states: fluid and insulator. None of these states has long-range spatial correlations, but this is a true albeit non-conventional phase transition because transport properties are singular at the transition point. In the fluid phase the mass transport is possible, whereas in the insulator phase it is completely blocked even at finite temperatures. We thus reveal how the interaction between disordered bosons influences their Anderson localization. This key question, first raised for electrons in solids, is now crucial for the studies of atomic bosons where recent experiments have demonstrated Anderson localization in expanding very dilute quasi-1D clouds.
We argue that giant jumps of current at finite voltages observed in disordered samples of InO, TiN and YSi manifest a bistability caused by the overheating of electrons. One of the stable states is overheated and thus low-resistive, while the other,
high-resistive state is heated much less by the same voltage. The bistability occurs provided that cooling of electrons is inefficient and the temperature dependence of the equilibrium resistance, R(T), is steep enough. We use experimental R(T) and assume phonon mechanism of the cooling taking into account its strong suppression by disorder. Our description of details of the I-V characteristics does not involve adjustable parameters and turns out to be in a quantitative agreement with the experiments. We propose experiments for more direct checks of this physical picture.
