Bose Glass Phase Research Articles

Self-induced Bose glass phase in quantum quasicrystals

We study the emergence of Bose glass phases in self sustained bosonic quasicrystals induced by a pair interaction between particles of Lifshitz–Petrich type. By using a mean-field variational method designed in momentum space as well as Gross–Pitaevskii simulations we determine the phase diagram of the model. The study of the local and global superfluid fraction allows the identification of supersolid, super quasicrystal, Bose glass and insulating phases. The Bose glass phase emerges as a quasicrystal phase in which the global superfluidity is essentially zero, while the local superfluidity remains finite in certain ring structures of the quasicrystalline pattern. Furthermore, we perform continuous space Path Integral Monte Carlo simulations for a case in which the interaction between particles stabilizes a quasicrystal phase. Our results show that as the strength of the interaction between particles is increased the system undergoes a sequence of states consistent with the super quasicrystal, Bose glass, and quasicrystal insulator thermodynamic phases.

Strong-coupling mean-field and classical percolation approach to produce the phase diagram of disordered Bose–Hubbard model at fixed n = 1 filling

We perform strong-coupling mean-field along with classical percolation analysis to produce the phase diagram of disordered Bose–Hubbard model with chemical potential disorder in two dimensional square lattice. The phase diagram in the disorder strength (Δ) and the on-site repulsion (U), for two and three dimensional system at fixed n = 1 filling show interesting re-entrant superfluid phase sandwiched between Bose-glass phases, as observed by the previous QMC results. We produce the phase diagram exhibiting the re-entrant phenomenon as well as phenomenologically demonstrate the robustness of the re-entrant phenomena within this method. We also discuss the importance of the method and applicability in further analysis of the same phase diagram.

Tomonaga-Luttinger liquid–Bose-glass phase transition in a system of one-dimensional disordered fermions with pair hoppings

Tomonaga-Luttinger liquid–Bose-glass phase transition in a system of one-dimensional disordered fermions with pair hoppings

Contour-time approach to the disordered Bose-Hubbard model in the strong coupling regime

There has been considerable interest in the disordered Bose Hubbard model (BHM) in recent years, particularly in the context of thermalization and many-body localization. We develop a two-particle irreducible (2PI) strong-coupling approach to the disordered BHM that allows us to treat both equilibrium and out-of-equilibrium situations. We obtain equations of motion for spatio-temporal correlations and explore their equilibrium solutions. We study the equilibrium phase diagram as a function of disorder strength and discuss applications of the formalism to out-of-equilibrium situations. We also note that the disorder strengths where the emergence of non-ergodic dynamics was observed in a recent experiment [Choi et al. (2016) [61]] appear to correspond to the Mott insulator – Bose Glass phase boundary.

Emergence of damped-localized excitations of the Mott state due to disorder

A key aspect of ultracold bosonic quantum gases in deep optical lattice potential wells is the realization of the strongly interacting Mott insulating phase. Many characteristics of this phase are well understood, however little is known about the effects of a random external potential on its gapped quasiparticle and quasihole low-energy excitations. In the present study we investigate the effect of disorder upon the excitations of the Mott insulating state at zero temperature described by the Bose–Hubbard model. Using a field-theoretical approach we obtain a resummed expression for the disorder ensemble average of the spectral function. Its analysis shows that disorder leads to an increase of the effective mass of both quasiparticle and quasihole excitations. Furthermore, it yields the emergence of damped states, which exponentially decay during propagation in space and dominate the whole band when disorder becomes comparable to interactions. We argue that such damped-localized states correspond to single-particle excitations of the Bose-glass phase.

Thermodynamic Phase Diagram of Two-Dimensional Bosons in a Quasicrystal Potential.

Quantum simulation of quasicrystals in synthetic bosonic matter now paves the way for the exploration of these intriguing systems in wide parameter ranges. Yet thermal fluctuations in such systems compete with quantum coherence and significantly affect the zero-temperature quantum phases. Here we determine the thermodynamic phase diagram of interacting bosons in a two-dimensional, homogeneous quasicrystal potential. We find our results using quantum MonteCarlo simulations. Finite-size effects are carefully taken into account and the quantum phases are systematically distinguished from thermal phases. In particular, we demonstrate stabilization of a genuine Bose glass phase against the normal fluid in sizable parameter ranges. We interpret our results for strong interactions using a fermionization picture and discuss experimental relevance.

Angle-dependent Magnetoresistance of an Ordered Bose Glass of Vortices in YBa2Cu3O7-δ Thin Films with a Periodic Pinning Lattice

The competition between intrinsic disorder in superconducting YBa2Cu3O7−δ (YBCO) thin films and an ultradense triangular lattice of cylindrical pinning centers spaced at 30 nm intervals results in an ordered Bose glass phase of vortices. The samples were created by scanning the focused beam of a helium-ion microscope over the surface of the YBCO thin film to form columns of point defects where superconductivity was locally suppressed. The voltage–current isotherms reveal critical behavior and scale in the vicinity of the second-order glass transition. The latter exhibits a distinct peak in melting temperature (Tg) vs. applied magnetic field (Ba) at the magnetic commensurability field, along with a sharp rise in the lifetimes of glassy fluctuations. Angle-dependent magnetoresistance measurements in constant-Lorentz-force geometry unveil a strong increase in anisotropy compared to a pristine reference film where the density of vortices matches that of the columnar defects. The pinning is therefore, dominated by the magnetic-field component parallel to the columnar defects, exposing its one-dimensional character. These results support the idea of an ordered Bose glass phase.

Quantum transitions from superfluid to insulating phases in disordered Bose systems

By the example of Heisenberg d-dimensional disordered non-frustrated antiferromagnets, we discuss quantum transitions at d≥2 from magnetically ordered (superfluid) to various disorder-induced insulating phases (Bose-glass, Mott-glass, etc.) in Bose systems with quenched disorder. We perform a scaling consideration as well as a discussion based on the hydrodynamic description of long-wavelength excitations and on the assumption that the ordered part of the system shows fractal properties near the transition point. We propose that the scaling ansatz for the singular part of the free energy suggested before for the transition to the Bose-glass phase is applicable also for other transitions if the quenched disorder does not produce a local imbalance in sublattices magnetizations. We show using the scaling consideration that η=2−z and β=νd/2, where η, β, and ν, are critical exponents of the correlation function, the order parameter, and the correlation length, respectively, and z is the dynamical critical index. These relations were missed in previous analytical discussions of Bose-glass and Mott-glass phases. They signify, in particular, that z=d/2 for the transition to the Mott-glass phase and that the density of states of localized excitations shows a superuniversal (i.e., independent of d) behavior near the transitions. Being derived solely from the scaling analysis, the above relations for η and β are valid also for the transition to the random-singlet phase.

Unusual fluid of one-dimensional disordered bosons at finite temperature

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 ${E}_{K}$ versus $\ensuremath{\gamma}$ at various $T$ signals a transition by its convergence towards a common value. ${E}_{K}$ 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 ${E}_{K}$ 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 ${g}_{2}(0)$, and ${E}_{K}$. Surprisingly, the diffusion constant ${D}_{0}$ 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.

Finite-temperature phases of trapped bosons in a two-dimensional quasiperiodic potential

We study a system of 2D trapped bosons in a quasiperiodic potential via ab initio Path Integral Monte Carlo simulations, focusing on its finite temperature properties, which have not yet been explored. Alongside the superfluid, normal fluid and insulating phases, we demonstrate the existence of a Bose glass phase, which is found to be robust to thermal fluctuations, up to about half of the critical temperature of the non-interacting system. Local quantities in the trap are characterized by employing zonal estimators, allowing us to trace a phase diagram; we do so for a set of parameters within reach of current experiments with quasi-2D optical confinement.

The mean-field Bose glass in quasicrystalline systems

We confirm the presence of a mean-field Bose glass (BG) in 2D quasicrystalline Bose–Hubbard models. We focus on two models where the aperiodic component is present in different parts of the problem. First, we consider a 2D generalisation of the Aubry–André (AA) model, where the lattice geometry is that of a square with a quasiperiodic onsite potential. Second, we consider the randomly disordered vertex model, which takes aperiodic tilings with non-crystalline rotational symmetries, and forms lattices from the vertices and lengths of the tiles. For the disordered vertex models, the mean-field BG forms across large ranges of the chemical potential, and we observe no significant differences from the case of a square lattice with uniform random disorder. Small variations in the critical points in the presence of random disorder between quasicrystalline and crystalline lattice geometries can be accounted for by the varying coordination number and the different rotational symmetries present. In the 2D AA model, substantial differences are observed from the usual phase diagrams of crystalline disordered systems. We show that weak modulation lines can be predicted from the underlying potential and may stabilise or suppress the mean-field BG in certain regimes. This results in a lobe-like structure for the mean-field BG in the 2D AA model, which is significantly different from the case of random disorder. Together, the two quasicrystalline models studied in this work show that the mean-field BG phase is present, as expected for 2D quasiperiodic models. However, a quasicrystalline geometry is not sufficient to result in differences from crystalline realisations of the BG, whereas a quasiperiodic form of disorder can result in different physics, as we observe in the 2D AA model.

Quench spectroscopy of a disordered quantum system

The characterization of excitations in disordered quantum systems is a central issue in connection with glass physics and many-body localization. Here, we show that quench spectroscopy of a disordered model, as realized from its out-of-equilibrium dynamics following a global quench, allows us to fully characterize the spectral properties of the disordered phases. In the Bose-Hubbard model, a clear signature of gapless excitations in momentum-resolved spectroscopy enables us to accurately locate the Mott insulator to Bose glass transition, while the presence or absence of a well-defined soundlike mode distinguishes the superfluid from the Bose glass phase. Moreover, spatially-resolved spectroscopy provides local spectral properties and allows us to extract the typical spacing of gapless regions, giving a second independent way to uniquely identify all three phases. Our findings have far-ranging implications for a variety of experimental platforms, and offer a powerful and versatile probe of the low-energy phases of disordered systems.

Finding the phase diagram of strongly correlated disordered bosons using quantum quenches

The question of how the low-energy properties of disordered quantum systems may be connected to exotic localization phenomena at high energy is a key open question in the context of quantum glasses and many-body localization. In the preceding Letter [L. Villa, S. J. Thomson, and L. Sanchez-Palencia, preceding Letter, Phys. Rev. A 104, L021301 (2021)] we have shown that key features of the excitation spectrum of a disordered system can be efficiently probed from out-of-equilibrium dynamics following a quantum quench, providing distinctive signatures of the various phases. Here we extend this work by providing a more-in-depth study of the behavior of the quench spectral functions associated with different observables and investigating an extended parameter regime. We provide a detailed introduction to quench spectroscopy for disordered systems and show how spectral properties can be probed using both local operators and two-point correlation functions. We benchmark the technique using the one-dimensional Bose-Hubbard model in the presence of a random external potential, focusing on the low-lying excitations, and demonstrate that quench spectroscopy can distinguish the Mott insulator, superfluid, and Bose glass phases. We then explicitly reconstruct the zero-temperature phase diagram of the disordered Bose-Hubbard at fixed filling using two independent methods, experimentally accessible via both time-of-flight imaging and quantum gas microscopy, respectively, and demonstrate that quench spectroscopy can give valuable insights into the distribution of rare regions within disordered systems.

Green’s function approach to the Bose–Hubbard model with disorder

We analyse the distinction between the three different ground states presented by a system of spinless bosons with short-range interactions submitted to a random potential using the disordered Bose–Hubbard model. The criteria for identifying the superfluid, the Mott-insulator, and the Bose-glass phases at finite temperatures are discussed for small values of the kinetic energy associated with the tunnelling of particles between potential wells. Field theoretical considerations are applied in order to construct a diagrammatic hopping expansion to the finite-temperature Green’s function. By performing a summation of subsets of diagrams we are able to find the condition to the long-range correlations which leads to the phase boundary between superfluid and insulating phases. The perturbative expression to the local correlations allows us to calculate an approximation to the single-particle density of states of low-energy excitations in the presence of small hopping, which characterizes unambiguously the distinction between the Mott-insulator and the Bose-glass phases. We obtain the phase diagram for bounded on-site disorder. It is demonstrated that our analysis is capable of going beyond the mean-field theory results for the classification of these different ground states.

Chaos in the Bose-glass phase of a one-dimensional disordered Bose fluid.

We show that the Bose-glass phase of a one-dimensional disordered Bose fluid exhibits a chaotic behavior, i.e., an extreme sensitivity to external parameters. Using bosonization, the replica formalism and the nonperturbative functional renormalization group, we find that the ground state is unstable to any modification of the disorder configuration ("disorder" chaos) or variation of the Luttinger parameter ("quantum" chaos, analog to the "temperature" chaos in classical disordered systems). This result is obtained by considering two copies of the system, with slightly different disorder configurations or Luttinger parameters, and showing that intercopy statistical correlations are suppressed at length scales larger than an overlap length ξ_{ov}∼|ε|^{-1/α} (|ε|≪1 is a measure of the difference between the disorder distributions or Luttinger parameters of the two copies). The chaos exponent α can be obtained by computing ξ_{ov} or by studying the instability of the Bose-glass fixed point for the two-copy system when ε≠0. The renormalized, functional, intercopy disorder correlator departs from its fixed-point value-characterized by "cuspy" singularities-via a chaos boundary layer, in the same way as it approaches the Bose-glass fixed point when ε=0 through a quantum boundary layer. Performing a linear analysis of perturbations about the Bose-glass fixed point, we find α=1.

Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics, and spiked random matrices: Pinning and localization

We revisit the problem of an elastic line (such as a vortex line in a superconductor) subject to both columnar disorder and point disorder in dimension d=1+1. Upon applying a transverse field, a delocalization transition is expected, beyond which the line is tilted macroscopically. We investigate this transition in the fixed tilt angle ensemble and within a "one-way" model where backward jumps are neglected. From recent results about directed polymers in the mathematics literature, and their connections to random matrix theory, we find that for a single line and a single strong defect this transition in the presence of point disorder coincides with the Baik-Ben Arous-Péché (BBP) transition for the appearance of outliers in the spectrum of a perturbed random matrix in the Gaussian unitary ensemble. This transition is conveniently described in the polymer picture by a variational calculation. In the delocalized phase, the ground state energy exhibits Tracy-Widom fluctuations. In the localized phase we show, using the variational calculation, that the fluctuations of the occupation length along the columnar defect are described by f_{KPZ}, a distribution which appears ubiquitously in the Kardar-Parisi-Zhang universality class. We then consider a smooth density of columnar defect energies. Depending on how this density vanishes at its lower edge we find either (i) a delocalized phase only or (ii) a localized phase with a delocalization transition. We analyze this transition which is an infinite-rank extension of the BBP transition. The fluctuations of the ground state energy of a single elastic line in the localized phase (for fixed columnar defect energies) are described by a Fredholm determinant based on a new kernel, closely related to the kernel describing the largest real eigenvalues of the real Ginibre ensemble. The case of many columns and many nonintersecting lines, relevant for the study of the Bose glass phase, is also analyzed. The ground state energy is obtained using free probability and the Burgers equation. Connections with recent results on the generalized Rosenzweig-Porter model suggest that the localization of many polymers occurs gradually upon increasing their lengths.

Strongly Interacting Bosons in a Two-Dimensional Quasicrystal Lattice.

Quasicrystals exhibit exotic properties inherited from the self-similarity of their long-range ordered, yet aperiodic, structure. The recent realization of optical quasicrystal lattices paves the way to the study of correlated Bose fluids in such structures, but the regime of strong interactions remains largely unexplored, both theoretically and experimentally. Here, we determine the quantum phase diagram of two-dimensional correlated bosons in an eightfold quasicrystal potential. Using large-scale quantum MonteCarlo calculations, we demonstrate a superfluid-to-Bose glass transition and determine the critical line. Moreover, we show that strong interactions stabilize Mott insulator phases, some of which have spontaneously broken eightfold symmetry. Our results are directly relevant to current generation experiments and, in particular, drive prospects to the observation of the still elusive Bose glass phase in two dimensions and exotic Mott phases.

Bose-glass phase of a one-dimensional disordered Bose fluid: Metastable states, quantum tunneling, and droplets.

We study a one-dimensional disordered Bose fluid using bosonization, the replica method, and a nonperturbative functional renormalization-group approach. We find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale k, quantum tunneling between the ground state and low-lying metastable states leads to a rounding of the cusp singularity into a quantum boundary layer (QBL). The width of the QBL depends on an effective Luttinger parameter K_{k}∼k^{θ} that vanishes with an exponent θ=z-1 related to the dynamical critical exponent z. The QBL encodes the existence of rare "superfluid" regions, controls the low-energy dynamics, and yields a (dissipative) conductivity vanishing as ω^{2} in the low-frequency limit. These results reveal the glassy properties (pinning, "shocks," or static avalanches) of the Bose-glass phase and can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.

Phase diagrams of the disordered Bose-Hubbard model with cavity-mediated long-range and nearest-neighbor interactions

Recent experiments with ultracold atoms in an optical lattice have realized cavity-mediated long-range interaction and observed the emergence of a supersolid phase and a density wave phase in addition to Mott insulator and superfluid phases. Here we consider theoretically the effect of uncorrelated disorder on the phase diagram of this system and study the two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated diagonal disorder. We also study the phase diagram of the extended Bose-Hubbard model with nearest-neighbor interactions in the presence of uncorrelated diagonal disorder. The extended Bose-Hubbard model with nearest-neighbor interactions has been realized in the experiment using dipolar interaction recently. With the help of quantum Monte Carlo simulations using the worm algorithm, we determine the phase diagram of those two models. We compare the phase diagrams of cavity-mediated long-range interactions with nearest-neighbor interactions. We show that two kinds of Bose glass phases exist: one with and one without density wave order. We also find that weak disorder enhances the supersolid phase.Graphical abstract

The Effect of Disorder on the Phase Diagrams of Hard-Core Lattice Bosons With Cavity-Mediated Long-Range and Nearest-Neighbor Interactions

We use quantum Monte Carlo simulations with the worm algorithm to study the phase diagram of a two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated disorder in the hard-core limit. Our study shows the system is in a supersolid phase at weak disorder and a disordered solid phase at stronger disorder. Due to long-range interactions, a large region of metastable states exists in both clean and disordered systems. By comparing the phase diagrams for both clean and disordered systems, we find that disorder suppresses metastable states and superfluidity. We compare these results with the phase diagram of the extended Bose-Hubbard model with nearest-neighbor interactions. Here, the supersolid phase does not exist even at weak disorder. We identify two kinds of glassy phases: a Bose glass phase and a disordered solid phase. The glassy phases intervene between the density-wave and superfluid phases as the Griffiths phase of the Bose-Hubbard model. The disordered solid phase intervenes between the density-wave and Bose glass phases since both have a finite structure factor.