In previous important examinations by Aleiner et al. [Nat. Phys. 6, 900 (2010)] and Michal et al. [Proc. Natl. Acad. Sci. (U.S.A.) 113, E4455 (2016)], the fluid insulator transition has been explored in one-dimensional (1D) disordered bosons by analytical methods. However, the nature of this ``fluid'' is still not quite understood. Here we shed more light on this ``fluid'' by studying its properties under changes in the average particle number $\ensuremath{\langle}N\ensuremath{\rangle}$ and temperature
T in the absence of superfluidity. For this purpose, the worm algorithm path-integral Monte Carlo method is utilized in the grand-canonical ensemble. A measure for the width of path fluctuations is introduced that we call ${\ensuremath{\sigma}}_{J}$. It is found that by increasing $\ensuremath{\langle}N\ensuremath{\rangle}$, ${\ensuremath{\sigma}}_{J}$ rises as the bosons become less repulsive and gain more mobility. The compressibility $\ensuremath{\chi}(\ensuremath{\mu})$, $\ensuremath{\mu}$ being the chemical potential, reveals fluid behavior at the lower $\ensuremath{\gamma}$ and a proposed Bose-glass phase at the larger $\ensuremath{\gamma}$ (the Lieb-Liniger interaction parameter). The kinetic energy
EK versus $\ensuremath{\gamma}$ at various
T signals a transition by its convergence towards a common value.
EK versus $\ensuremath{\mu}$ reveals a peculiar inversion as one goes from small to larger values of the speckle strength $\ensuremath{\langle}V\ensuremath{\rangle}$ demonstrating a complex influence of the disorder. A tipover of
EK versus $\ensuremath{\gamma}$ from an increasing to a decreasing trend at the lower $\ensuremath{\gamma}$ also signals a transition. Further, Luttinger's liquid theory cannot be applied to describe 1D bosons in strong disorder at finite
T because of the absence of superfluidity. Moreover, $\ensuremath{\langle}V\ensuremath{\rangle}$ largely controls the behavior of $\ensuremath{\chi}(\ensuremath{\mu})$, the pair-correlation function at the origin
g2(0), and
EK. Surprisingly, the diffusion constant
D0 does not obey the classical isomorphism as it rises with
T. We also emphasize the importance of this work via its applicability to quantum wires.
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 coupling 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 study phase transitions in a two dimensional weakly interacting Bose gas in a random potential at finite temperatures. We identify superfluid, normal fluid, and insulator phases and construct the phase diagram. At T=0 one has a tricritical point where the three phases coexist. The truncation of the energy distribution at the trap barrier, which is a generic phenomenon in cold atom systems, limits the growth of the localization length and in contrast to the thermodynamic limit the insulator phase is present at any temperature.
We describe a renormalization group method to study the localized-delocalized transition of a one-dimensional interacting electron gas in a random potential. We obtain the phase diagram and the exponents of the correlation functions in the delocalized regime. The boundary between the two regimes is found to depend both on disorder and on the strength of the interactions. The delocalized phase is dominated by superconducting fluctuations. We find the asymptotic behaviour of the localization length and the temperature dependence of the conductivity. An analogous description is developed for the localized-superfluid transition of a one-dimensional boson gas. In this case the transition to the localized regime occurs for increasingly repulsive interactions.
We investigate the superfluid-insulator quantum phase transition of one-dimensional bosons with off-diagonal disorder by means of large-scale Monte Carlo simulations. For weak disorder, we find the transition to be in the same universality class as the superfluid-Mott insulator transition of the clean system. The nature of the transition changes for stronger disorder. Beyond a critical disorder strength, we find nonuniversal, disorder-dependent critical behavior. We compare our results to recent perturbative and strong-disorder renormalization group predictions. We also discuss experimental implications as well as extensions of our results to other systems.
The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension
dc which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on
4He absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.