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arXiv:2407.03430 · Physical Review A

Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas

N. Dupuis, Andrei A. Fedorenko

Published Oct 25, 2024• 3 citations
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Abstract

The authors explore the phase diagram of a one-dimensional Bose gas in the presence of disorder with long-range correlations decaying with distance. The disorder induces a Berezinskii-Kosterlitz-Thouless transition from a superfluid phase to a localized phase. The study reveals the conditions under which the ground state is a Mott glass, characterized by vanishing compressibility and gapless conductivity, rather than the usual Bose glass.

DOI
10.1103/physreva.110.l041304

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Physical review. B, Condensed matter•Jul 1, 1989•3,511 citations
The authors explore the phase diagram of a one-dimensional Bose gas in the presence of disorder with long-range correlations decaying with distance. The disorder induces a Berezinskii-Kosterlitz-Thouless transition from a superfluid phase to a localized phase. The study reveals the conditions under which the ground state is a Mott glass, characterized by vanishing compressibility and gapless conductivity, rather than the usual Bose glass.
We study the superfluid--Bose-glass transition in a one-dimensional lattice boson model with power-law decaying hopping amplitude ${t}_{i\ensuremath{-}j}\ensuremath{\sim}1/{|i\ensuremath{-}j|}^{\ensuremath{\alpha}}$, using bosonization and the nonperturbative functional renormalization group (FRG). When $\ensuremath{\alpha}$ is smaller than a critical value ${\ensuremath{\alpha}}_{c}<3$, the U(1) symmetry is spontaneously broken, which leads to a density mode with nonlinear dispersion and dynamical exponent $z=(\ensuremath{\alpha}\ensuremath{-}1)/2$; the superfluid phase is then stable for sufficiently weak disorder, contrary to the case of short-range hopping where disorder is a relevant perturbation when the Luttinger parameter is smaller than 3/23/23/2. In the presence of disorder, however, long-range hopping has no effect in the infrared limit and the FRG flow eventually becomes similar to that of a boson system with short-range hopping. This implies that the superfluid phase, when stable, exhibits a density mode with linear dispersion (z=1z=1z=1) and the superfluid--Bose-glass transition remains in the Berezinskii-Kosterlitz-Thouless universality class, while the Bose-glass fixed point is insensitive to long-range hopping. We compare our findings with a recent numerical study.
We study a one-dimensional disordered quantum fluid with linearly confining interactions (disordered Schwinger model) using bosonization and the nonperturbative functional renormalization group. We find that the long-range interactions make the Anderson-insulator (or, for bosons, the Bose-glass) fixed point (corresponding to a compressible state with a gapless optical conductivity) unstable, even if the latter may control the flow at intermediate energy scales. The stable fixed point describes an incompressible ground state with a gapped optical conductivity similar to a Mott insulator. These results disagree with the Gaussian variational method that predicts a Mott glass, namely a state with vanishing compressibility but a gapless optical conductivity.
The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.
We investigate the ground-state properties of quantum particles interacting via a long-range repulsive potential ${\mathcal{V}}_{\ensuremath{\sigma}}(x)\ensuremath{\sim}1/|x{|}^{1+\ensuremath{\sigma}}$ ($\ensuremath{-}1<\ensuremath{\sigma}$) or ${\mathcal{V}}_{\ensuremath{\sigma}}(x)\ensuremath{\sim}\ensuremath{-}|x{|}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\sigma}}$ ($\ensuremath{-}2\ensuremath{\le}\ensuremath{\sigma}<\ensuremath{-}1$) that interpolates between the Coulomb potential V0(x){\mathcal{V}}_{0}(x)V0​(x) and the linearly confining potential ${\mathcal{V}}_{\ensuremath{-}2}(x)$ of the Schwinger model. In the absence of disorder the ground state is a Wigner crystal when $\ensuremath{\sigma}\ensuremath{\le}0$. Using bosonization and the nonperturbative functional renormalization group we show that any amount of disorder suppresses the Wigner crystallization when $\ensuremath{-}3/2<\ensuremath{\sigma}\ensuremath{\le}0$; the ground state is then a Mott glass, i.e., a state that has a vanishing compressibility and a gapless optical conductivity. For $\ensuremath{\sigma}<\ensuremath{-}3/2$ the ground state remains a Wigner crystal.
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.
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.