Uncorrelated Disorder Research Articles

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.

Heat conduction in harmonic chains with Lévy-type disorder.

We consider heat transport in a one-dimensional harmonic chain attached at its ends to Langevin heat baths. The harmonic chain has mass impurities where the separation d between any two successive impurities is randomly distributed according to a power-law distribution P(d)∼1/d^{α+1}, being α>0. In the regime where the first moment of the distribution is well defined (1<α<2) the thermal conductivity κ scales with the system size N as κ∼N^{(α-3)/α} for fixed boundary conditions, whereas for free boundary conditions κ∼N^{(α-1)/α} if N≫1. When α=2, the inverse localization length λ scales with the frequency ω as λ∼ω^{2}lnω in the low-frequency regime, due to the logarithmic correction, the size scaling law of the thermal conductivity acquires a nonclosed form. When α>2, the thermal conductivity scales as in the uncorrelated disorder case. The situation α<1 is only analyzed numerically, where λ(ω)∼ω^{2-α}, which leads to the following asymptotic thermal conductivity: κ∼N^{-(α+1)/(2-α)} for fixed boundary conditions and κ∼N^{(1-α)/(2-α)} for free boundary conditions.

Hyperuniform vortex patterns at the surface of type-II superconductors

A many-particle system must posses long-range interactions in order to be hyperuniform at thermal equilibrium. Hydrodynamic arguments and numerical simulations show, nevertheless, that a three-dimensional elastic-line array with short-ranged repulsive interactions, such as vortex matter in a type-II superconductor, forms at equilibrium a class-II hyperuniform two-dimensional point pattern for any constant-$z$ cross section. In this case, density fluctuations vanish isotropically as $\sim q^{\alpha}$ at small wave-vectors $q$, with $\alpha=1$. This prediction includes the solid and liquid vortex phases in the ideal clean case, and the liquid in presence of weak uncorrelated disorder. We also show that the three-dimensional Bragg glass phase is marginally hyperuniform, while the Bose glass and the liquid phase with correlated disorder are expected to be non-hyperuniform at equilibrium. Furthermore, we compare these predictions with experimental results on the large-wavelength vortex density fluctuations of magnetically decorated vortex structures nucleated in pristine, electron-irradiated and heavy-ion irradiated superconducting BiSCCO samples in the mixed state. For most cases we find hyperuniform two-dimensional point patterns at the superconductor surface with an effective exponent $\alpha_{\text{eff}} \approx 1$. We interpret these results in terms of a large-scale memory of the high-temperature line-liquid phase retained in the glassy dynamics when field-cooling the vortex structures into the solid phase. We also discuss the crossovers expected from the dispersivity of the elastic constants at intermediate length-scales, and the lack of hyperuniformity in the $x\,-y$ plane for lengths $q^{-1}$ larger than the sample thickness due to finite-size effects in the $z$-direction.

Perfectly asymmetric Raman-Nath diffraction in disordered atomic gratings.

We investigate the effects of geometrical and structural disorders on perfectly asymmetric diffraction (PAD) in Raman-Nath regime. The two types of disorders are realized by introducing random fluctuations in the position and width of one-dimensional (1D) driven atomic lattices. Raman-Nath diffraction is modified differently with respect to the geometrical and structural disorders. It is shown that the PAD is observed with a certain strength range of geometrical disorder, exceeding which it can be destroyed, while the PAD is rather robust against structural disorder. The different behaviors originate from the disorder-induced random variations of the spatial phase shifts of the standing-wave (SW) coupling field and atomic lattices with Gaussian profile. Furthermore, we find that, in the presence of geometrical disorder, the PAD is more susceptible to correlated disorder than to uncorrelated disorder. Our scheme may be useful for understanding the effects of disorder on the diffraction of light and matter waves in disordered potentials..

Impact of speckle disorder on a superfluid Fermi system

Optical lattice experiments which probe the effect of disorder on superfluidity often use a speckle pattern for generating the disorder. Such speckle disorder is spatially correlated. While fermionic superfluidity in the presence of uncorrelated disorder is well studied, the impact of correlated disorder, particularly on thermal properties of the superfluid, is poorly understood. We provide a detailed study of the impact of speckle disorder, for varying speckle size and disorder magnitude, on the ground state and thermal properties of a Fermi superfluid. We work in the strong coupling regime of BCS-BEC crossover in a two dimensional lattice. For a fixed disorder strength, an increase in speckle size leads to smoothening of the self-consistent background potential, increase in the critical disorder needed for a superfluid-insulator transition, and an increase in superfluid $T_c$ . Along with these hints at decrease in effective disorder, speckle correlations also suppress the superfluid gap and the gap formation temperature - effects normally associated with increasing disorder. We correlate these effects with the effective potential and the single particle localisation effects in the ground state

One-Dimensional Quasicrystals with Power-Law Hopping.

One-dimensional quasiperiodic systems with power-law hopping, 1/r^{a}, differ from both the standard Aubry-André (AA) model and from power-law systems with uncorrelated disorder. Whereas in the AA model all single-particle states undergo a transition from ergodic to localized at a critical quasidisorder strength, short-range power-law hops with a>1 can result in mobility edges. We find that there is no localization for long-range hops with a≤1, in contrast to the case of uncorrelated disorder. Systems with long-range hops rather present ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but nonergodic) states. Both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.

Spin-polarized localization in a magnetized chain

We investigate a simple tight-binding Hamiltonian to understand the stability of spin-polarized transport of states with an arbitrary spin content in the presence of disorder. The general spin state is made to pass through a linear chain of magnetic atoms, and the localization lengths are computed. Depending on the value of spin, the chain of magnetic atoms unravels a hidden transverse dimensionality that can be exploited to engineer energy regimes where only a selected spin state is allowed to retain large localization lengths. We carry out a numerical anmalysis to understand the roles played by the spin projections in different energy regimes of the spectrum. For this purpose, we introduce a new measure, dubbed spin-resolved localization length. We study uncorrelated disorder in the potential profile offered by the magnetic substrate or in the orientations of the magnetic moments concerning a given direction in space. Our results show that the spin filtering effect is robust against weak disorder and hence the proposed system should be a good candidate model for experimental realizations of spin-selective transport devices.

Correlation-induced localization

A new paradigm of Anderson localization caused by correlations in the long-range hopping along with uncorrelated on-site disorder is considered which requires a more precise formulation of the basic localization-delocalization principles. A new class of random Hamiltonians with translation-invariant hopping integrals is suggested and the localization properties of such models are established both in the coordinate and in the momentum spaces alongside with the corresponding level statistics. Duality of translation-invariant models in the momentum and coordinate space is uncovered and exploited to find a full localization-delocalization phase diagram for such models. The crucial role of the spectral properties of hopping matrix is established and a new matrix inversion trick is suggested to generate a one-parameter family of equivalent localization/delocalization problems. Optimization over the free parameter in such a transformation together with the localization/delocalization principles allows to establish exact bounds for the localized and ergodic states in long-range hopping models. When applied to the random matrix models with deterministic power-law hopping this transformation allows to confirm localization of states at all values of the exponent in power-law hopping and to prove analytically the symmetry of the exponent in the power-law localized wave functions.

Disordered XY model: Effective medium theory and beyond

We study the effect of uncorrelated random disorder on the temperature dependence of the superfluid stiffness in the two-dimensional classical XY model. By means of a perturbative expansion in the disorder potential, equivalent to the T-matrix approximation, we provide an extension of the effective-medium-theory result able to describe the low-temperature stiffness, and its separate diamagnetic and paramagnetic contributions. These analytical results provide an excellent description of the Monte Carlo simulations for two prototype examples of uncorrelated disorder. Our findings offer an interesting perspective on the effects of quenched disorder on longitudinal phase fluctuations in two-dimensional superfluid systems.

Magnetism in cation-disordered 3d−4d/5d double perovskites

Employing an exact diagonalization Monte Carlo solution of the first-principles-derived model Hamiltonian of a number of ${A}_{2}B{B}^{\ensuremath{'}}{\mathrm{O}}_{6}$ double-perovskite compounds, containing a $3d$ transition metal at the $B$ site and a $4d$ or $5d$ transition metal ion at the ${B}^{\ensuremath{'}}$ site, we investigate the effect of $B/{B}^{\ensuremath{'}}$ cation disorder on their magnetic properties. Our exhaustive study reveals that the influence of cation disorder on both the magnetic transition temperature and magnetization depends strongly on the underlying exchange mechanism with a distinct difference between the double exchange mechanism and a combined double exchange and superexchange mechanism. We further find that the nature of the disorder has a remarkable effect. While the uncorrelated or random disorder has a severely detrimental effect, especially for magnetism having a superexchange contribution, correlated disorder with a high degree of short-range order retains the magnetic properties of the fully cation-ordered compounds to a large extent. Our findings shed light on the puzzling report of magnetic order in fully cation-disordered CrRu oxides.

Correlated electronic structure with uncorrelated disorder

We introduce a computational scheme for calculating the electronic structure of random alloys that includes electronic correlations within the framework of the combined density functional and dynamical mean-field theory. By making use of the particularly simple parameterization of the electron Green's function within the linearized muffin-tin orbitals method, we show that it is possible to greatly simplify the embedding of the self-energy. This in turn facilitates the implementation of the coherent potential approximation, which is used to model the substitutional disorder. The computational technique is tested on the Cu-Pd binary alloy system, and for disordered Mn-Ni interchange in the half-metallic NiMnSb.

Enhanced non-Markovian behavior in quantum walks with Markovian disorder

Non-Markovian quantum effects are typically observed in systems interacting with structured reservoirs. Discrete-time quantum walks are prime example of such systems in which, quantum memory arises due to the controlled interaction between the coin and position degrees of freedom. Here we show that the information backflow that quantifies memory effects can be enhanced when the particle is subjected to uncorrelated static or dynamic disorder. The presence of disorder in the system leads to localization effects in 1-dimensional quantum walks. We shown that it is possible to infer about the nature of localization in position space by monitoring the information backflow in the reduced system. Further, we study other useful properties of quantum walk such as entanglement, interference and its connection to quantum non-Markovianity.

Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice.

A single-particle mobility edge (SPME) marks a critical energy separating extended from localized states in a quantum system. In one-dimensional systems with uncorrelated disorder, a SPME cannot exist, since all single-particle states localize for arbitrarily weak disorder strengths. However, in a quasiperiodic system, the localization transition can occur at a finite detuning strength and SPMEs become possible. In this Letter, we find experimental evidence for the existence of such a SPME in a one-dimensional quasiperiodic optical lattice. Specifically, we find a regime where extended and localized single-particle states coexist, in good agreement with theoretical simulations, which predict a SPME in this regime.

A generic phase between disordered Weyl semimetal and diffusive metal

Quantum phase transitions of three-dimensional (3D) Weyl semimetals (WSMs) subject to uncorrelated on-site disorder are investigated through quantum conductance calculations and finite-size scaling of localization length. Contrary to previous claims that a direct transition from a WSM to a diffusive metal (DM) occurs, an intermediate phase of Chern insulator (CI) between the two distinct metallic phases should exist due to internode scattering that is comparable to intranode scattering. The critical exponent of localization length is ν,simeq 1.3 for both the WSM-CI and CI-DM transitions, in the same universality class of 3D Gaussian unitary ensemble of the Anderson localization transition. The CI phase is confirmed by quantized nonzero Hall conductances in the bulk insulating phase established by localization length calculations. The disorder-induced various plateau-plateau transitions in both the WSM and CI phases are observed and explained by the self-consistent Born approximation. Furthermore, we clarify that the occurrence of zero density of states at Weyl nodes is not a good criterion for the disordered WSM, and there is no fundamental principle to support the hypothesis of divergence of localization length at the WSM-DM transition.

Localization and hybridization across an effective mobility edge in periodically driven speckle potentials

Disorder in a 1D quantum lattice induces Anderson localization of the eigenstates and blocks transport through the lattice. A time-periodic drive, when applied to a lattice with uncorrelated disorder, typically increases (as compared to the stationary states) localization length of the appearing Floquet states. We go beyond the uncorrelated disorder limit and address the experimentally relevant case of speckle potentials in which spatial correlations in on-site disorder are present. These correlations are responsible for the creation of an effective mobility edge in the spectrum of the stationary lattice Hamiltonian. We find that a slow driving leads to resonant hybridization of the Floquet states across the edge; i.e., it increases the width of the states in the localized band and decreases it for the states in the quasi-extended band. By increasing the drive amplitude, we observe homogenization of the bands so that finally all Floquet states become weakly localized and sparse.

One‐particle density matrix characterization of many‐body localization

We study interacting fermions in one dimension subject to random, uncorrelated onsite disorder, a paradigmatic model of many‐body localization (MBL). This model realizes an interaction‐driven quantum phase transition between an ergodic and a many‐body localized phase, with the transition occurring in the many‐body eigenstates. We propose a single‐particle framework to characterize these phases by the eigenstates (the natural orbitals) and the eigenvalues (the occupation spectrum) of the one‐particle density matrix (OPDM) in individual many‐body eigenstates. As a main result, we find that the natural orbitals are localized in the MBL phase, but delocalized in the ergodic phase. This qualitative change in these single‐particle states is a many‐body effect, since without interactions the single‐particle energy eigenstates are all localized. The occupation spectrum in the ergodic phase is thermal in agreement with the eigenstate thermalization hypothesis, while in the MBL phase the occupations preserve a discontinuity at an emergent Fermi edge. This suggests that the MBL eigenstates are weakly dressed Slater determinants, with the eigenstates of the underlying Anderson problem as reference states. We discuss the statistical properties of the natural orbitals and of the occupation spectrum in the two phases and as the transition is approached. Our results are consistent with the existing picture of emergent integrability and localized integrals of motion, or quasiparticles, in the MBL phase. We emphasize the close analogy of the MBL phase to a zero‐temperature Fermi liquid: in the studied model, the MBL phase is adiabatically connected to the Anderson insulator and the occupation‐spectrum discontinuity directly indicates the presence of quasiparticles localized in real space. Finally, we show that the same picture emerges for interacting fermions in the presence of an experimentally‐relevant bichromatic lattice and thereby demonstrate that our findings are not limited to a specific model. image

Full counting statistics in the Haldane-Shastry chain

We present analytical and numerical results regarding the magnetization full counting statistics (FCS) of a subsystem in the ground-state of the Haldane-Shastry chain. Exact Pfaffian expressions are derived for the cumulant generating function, as well as any observable diagonal in the spin basis. In the limit of large systems, the scaling of the FCS is found to be in agreement with the Luttinger liquid theory. The same techniques are also applied to inhomogeneous deformations of the chain. This introduces a certain amount of disorder in the system; however we show numerically that this is not sufficient to flow to the random singlet phase, that corresponds to $XXZ$ chains with uncorrelated bond disorder.

Slow relaxation and sensitivity to disorder in trapped lattice fermions after a quench

We consider a system of non-interacting fermions in one dimension subject to a single-particle potential consisting of (a) a strong optical lattice, (b) a harmonic trap, and (c) uncorrelated on-site disorder. After a quench, in which the center of the harmonic trap is displaced, we study the occupation function of the fermions and the time-evolution of experimental observables. Specifically, we present numerical and analytical results for the post-quench occupation function of the fermions, and analyse the time-evolution of the real-space density profile. Unsurprisingly for a non-interacting (and therefore integrable) system, the infinite-time limit of the density profile is non-thermal. However, due to Bragg-localization of the higher-energy single-particle states, the approach to even this non-thermal state is extremely slow. We quantify this statement, and show that it implies a sensitivity to disorder parametrically stronger than that expected from Anderson localization.

Transport and localization in a topological phononic lattice with correlated disorder

Recently proposed classical analogs of topological insulators in phononic lattices have the advantage of much more accessible experimental realization as compared to conventional materials. Drawn to their potential practical structural applications, we investigate how disorder, which is generically non-negligible in macroscopic realization, can attenuate the topologically protected edge (TPE) modes that constitute robust transmitting channels at zero disorder. We simulate the transmission of phonon modes in a quasi-one-dimensional classical lattice waveguide with mass disorder, and show that the TPE mode transmission remains highly robust ($\Xi\sim1$) in the presence of uncorrelated disorder, but diminishes when disorder is spatially correlated. This reduction in transmittance is attributed to the Anderson localization of states within the mass disorder domains. By contrast, non-TPE channels exhibit qualitatively different behavior, with spatial correlation in the mass disorder leading to significant transmittance reduction (enhancement) at low (high) frequencies. Our results demonstrate how topologically protected edge modes drastically modify the effect of spatial correlation on mode localization.

Influence of complex disorder on skew-scattering Hall effects inL10-ordered FePt alloy

We show by first-principles calculations that the skew-scattering anomalous Hall and spin-Hall angles of L$1_0$-ordered FePt drastically depend on different types of disorder. A different sign of the AHE is obtained when slightly deviating from the stoichiometric ratio towards the Fe-rich side as compared to the Pt-rich side. For stoichiometric samples, short-range ordering of defects has a profound effect on the Hall angles and can change them by a factor of $2$ as compared to the case of uncorrelated disorder. This might explain the vast range of anomalous Hall angles measured in experiments, which undergo different preparation procedures and thus might differ in their crystallographic quality.