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arXiv:cond-mat/0611109

Disorder-Induced Superfluidity in Hardcore Bosons in Two Dimensions

Ji-Woo Lee, Shailesh Chandrasekharan A, Harold U. Baranger

Published Nov 4, 2006• 0 citations
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Abstract

We study the effect of disorder on hardcore bosons in two dimensions at the SU(2) symmetric ``Heisenberg point''. We obtain our results with quantum Monte Carlo simulations using the directed loop algorithm. In the absence of disorder, the system has no long-range order at finite temperature due to the enhanced symmetry. However, the introduction of a disordered potential, uniformly distributed from -D to D, induces a finite-temperature superfluid phase. In particular the diagonal correlation length ξdecreases but the superfluid order-parameter correlation function becomes a power-law. A non-monotonic finite-size behavior is noted and explained as arising due to ξ. We provide evidence that at long distances the effects of a weak disordered potential can be mimicked by an effective uniform potential with a root-mean-square value: mu_eff = D/sqrt{3}. For strong disorder, the system becomes a Bose glass insulator.

DOI
10.48550/arxiv.cond-mat/0611109

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We study the effect of disorder on hardcore bosons in two dimensions at the SU(2) symmetric ``Heisenberg point''. We obtain our results with quantum Monte Carlo simulations using the directed loop algorithm. In the absence of disorder, the system has no long-range order at finite temperature due to the enhanced symmetry. However, the introduction of a disordered potential, uniformly distributed from -D to D, induces a finite-temperature superfluid phase. In particular the diagonal correlation length ξdecreases but the superfluid order-parameter correlation function becomes a power-law. A non-monotonic finite-size behavior is noted and explained as arising due to ξ. We provide evidence that at long distances the effects of a weak disordered potential can be mimicked by an effective uniform potential with a root-mean-square value: mu_eff = D/sqrt{3}. For strong disorder, the system becomes a Bose glass insulator.
We present results of path-integral Monte Carlo simulations of bosons on a two-dimensional square lattice in a random potential of average strength V and with on-site repulsion U. We find that the superfluid density ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$ is enhanced by increasing V and U in certain regions of parameter space. By combining the results of ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$, with the behavior of the density-density correlation function on lattices of size up to 10\ifmmode\times\else\texttimes\fi{}10, we study the superfluid--to--Mott-insulator transition and the transition from a superfluid to a disorder-localized (``Bose glass'') phase.
We consider a one-dimensional system of interacting bosons in a random potential. At zero temperature, it can be either in the superfluid or in the insulating phase. We study the transition at weak disorder and moderate interaction. Using a systematic approach, we derive the renormalization group equations at two-loop order and discuss the phase diagram. We find the universal form of the correlation functions at the transitions and compute the logarithmic corrections to the main universal power-law behavior. In order to mimic large density fluctuations on a single site, we study a simplified model of disordered two-leg bosonic ladders with correlated disorder across the rung. Contrarily to the single-chain case, the latter system exhibits a transition between a superfluid and a localized phase where the exponents of the correlation functions at the transition do not take universal values.
We use quantum Monte Carlo simulations to study the effect of disorder, in the form of a disordered chemical potential, on the phase diagram of the hard-core Bosonic Hubbard model in two dimensions. We find numerical evidence that in two dimensions, no matter how weak the disorder, it will always destroy the long-range density wave order (checkerboard solid) present at half filling and strong nearest-neighbor repulsion and replace it with a bose glass phase. We study the properties of this glassy phase including the superfluid density, energy gaps, and the full Green's function. We also study the possibility of other localized phases at weak nearest-neighbor repulsion, i.e., Anderson localization. We find that such a phase does not truly exist: The disorder must exceed a threshold before the bosons (at weak nearest-neighbor repulsion) are localized. The phase diagram for hard-core bosons with disorder cannot be obtained easily from the soft-core phase diagram discussed in the literature.
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{d}_{c}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^{4}\mathrm{He}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.
We study the phase diagram of two-dimensional, interacting bosons in the presence of a correlated disorder in continuous space, by using large-scale quantum Monte Carlo simulations at finite temperature. We show that the superfluid transition is strongly protected against disorder. It remains of the Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the chemical potential. Moreover, we study the transport properties in the strong disorder regime where a zero-temperature Bose-glass phase is expected. We show that the conductance exhibits a thermally activated behavior vanishing only at zero temperature. Our results point towards the existence of a Bose bad-metal phase as a precursor of the Bose-glass phase.