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arXiv2014

Recurrent scattering and memory effect at the Anderson localization transition

We report on ultrasonic measurements of the propagation operator in a strongly scattering mesoglass. The backscattered field is shown to display a deterministic spatial coherence due to a remarkably large memory effect induced by long recurrent trajectories. Investigation of the recurrent scattering contribution directly yields the probability for a wave to come back close to its starting spot. The decay of this quantity with time is shown to change dramatically near the Anderson localization transition. The singular value decomposition of the propagation operator reveals the dominance of very intense recurrent scattering paths near the mobility edge.

cond-mat.dis-nn↗

arXiv2014

Pseudolikelihood Decimation Algorithm Improving the Inference of the Interaction Network in a General Class of Ising Models

In this Letter we propose a new method to infer the topology of the interaction network in pairwise models with Ising variables. By using the pseudolikelihood method (PLM) at high temperature, it is generally possible to distinguish between zero and nonzero couplings because a clear gap separate the two groups. However at lower temperatures the PLM is much less effective and the result depends on subjective choices, such as the value of the $\ell_1$ regularizer and that of the threshold to separate nonzero couplings from null ones. We introduce a decimation procedure based on the PLM that recursively sets to zero the less significant couplings, until the variation of the pseudolikelihood signals that relevant couplings are being removed. The new method is fully automated and does not require any subjective choice by the user. Numerical tests have been performed on a wide class of Ising models, having different topologies (from random graphs to finite dimensional lattices) and different couplings (both diluted ferromagnets in a field and spin glasses). These numerical results show that the new algorithm performs better than standard PLM

cond-mat.dis-nn↗

arXiv2013

Observation of infinite-range intensity correlations above, at and below the 3D Anderson localization transition

We investigate long-range intensity correlations on both sides of the Anderson transition of classical waves in a three-dimensional (3D) disordered material. Our ultrasonic experiments are designed to unambiguously detect a recently predicted infinite-range C0 contribution, due to local density of states fluctuations near the source. We find that these C0 correlations, in addition to C2 and C3 contributions, are significantly enhanced near mobility edges. Separate measurements of the inverse participation ratio reveal a link between C0 and the anomalous dimension Δ_2, implying that C0 may also be used to explore the critical regime of the Anderson transition.

cond-mat.dis-nn↗

arXiv2014

Soft modes and non-affine rearrangements in the inherent structures of supercooled liquids

We find that the hierarchical organization of the potential energy landscape in a model supercooled liquid can be related to a change in the spatial distribution of soft normal modes. For groups of nearby minima, between which fast relaxation processes typically occur, the localization of the soft modes is very similar. The spatial distribution of soft regions changes, instead, for minima between which transitions relevant to structural relaxation occur. This may be the reason why the soft modes are able to predict spatial heterogeneities in the dynamics. Nevertheless, the very softest modes are only weakly correlated with dynamical heterogeneities, and instead show higher statistical overlap with regions in the local minima that would undergo non-affine rearrangements if subjected to a shear deformation. This feature of the supercooled liquid is reminiscent of the behavior of non-affine deformations in amorphous solids, where the very softest modes identify the {\it loci} of plastic instabilities.

cond-mat.dis-nn↗

arXiv2014

Inhibition causes ceaseless dynamics in networks of excitable nodes

The collective dynamics of a network of excitable nodes changes dramatically when inhibitory nodes are introduced. We consider inhibitory nodes which may be activated just like excitatory nodes but, upon activating, decrease the probability of activation of network neighbors. We show that, although the direct effect of inhibitory nodes is to decrease activity, the collective dynamics becomes self-sustaining. We explain this counterintuitive result by defining and analyzing a "branching function" which may be thought of as an activity-dependent branching ratio. The shape of the branching function implies that for a range of global coupling parameters dynamics are self-sustaining. Within the self-sustaining region of parameter space lies a critical line along which dynamics take the form of avalanches with universal scaling of size and duration, embedded in ceaseless timeseries of activity. Our analyses, confirmed by numerical simulation, suggest that inhibition may play a counterintuitive role in excitable networks.

q-bio.NC↗

arXiv2014

Finite-temperature conductivity and magnetoconductivity of topological insulators

The electronic transport experiments on topological insulators exhibit a dilemma. A negative cusp in magnetoconductivity is widely believed as a quantum transport signature of the topological surface states, which are immune from localization and exhibit the weak antilocalization. However, the measured conductivity drops logarithmically when lowering temperature, showing a typical feature of the weak localization as in ordinary disordered metals. Here, we present a conductivity formula for massless and massive Dirac fermions as a function of magnetic field and temperature, by taking into account the electron-electron interaction and quantum interference simultaneously. The formula reconciles the dilemma by explicitly clarifying that the temperature dependence of the conductivity is dominated by the interaction while the magnetoconductivity is mainly contributed by the quantum interference. The theory paves the road to quantitatively study the transport in topological insulators and other two-dimensional Dirac-like systems, such as graphene, transition metal dichalcogenides, and silicene.

cond-mat.mes-hall↗

arXiv2014

Pure scaling operators at the integer quantum Hall plateau transition

Stationary wave functions at the transition between plateaus of the integer quantum Hall effect are known to exhibit multi-fractal statistics. Here we explore this critical behavior for the case of scattering states of the Chalker-Coddington model with point contacts. We argue that moments formed from the wave amplitudes of critical scattering states decay as pure powers of the distance between the points of contact and observation. These moments in the continuum limit are proposed to be correlations functions of primary fields of an underlying conformal field theory. We check this proposal numerically by finite-size scaling. We also verify the CFT prediction for a 3-point function involving two primary fields.

cond-mat.dis-nn↗

arXiv2013

Dynamical quantum phase transitions in random spin chains

Quantum systems can exhibit a great deal of universality at low temperature due to the structure of ground states and the critical points separating distinct states. On the other hand, quantum time evolution of the same systems involves all energies and it is therefore thought to be much harder, if at all possible, to have sharp transitions in the dynamics. In this paper we show that phase transitions characterized by universal singularities do occur in the time evolution of random spin chains. The sharpness of the transitions and integrity of the phases owes to many-body localization, which prevents thermalization in these systems. Using a renormalization group approach, we solve the time evolution of random Ising spin chains with generic interactions starting from initial states of arbitrary energy. As a function of the Hamiltonian parameters, the system is tuned through a dynamical transition, similar to the ground state critical point, at which the local spin correlations establish true long range temporal order. In the state with dominant transverse field, a spin that starts in an up state loses its orientation with time, while in the "ordered" state it never does. As in ground state quantum phase transitions, the dynamical transition has unique signatures in the entanglement properties of the system. When the system is initialized in a product state the entanglement entropy grows as $log(t)$ in the two "phases", while at the critical point it grows as $log^\a(t)$, with $\a$ a universal number. This universal entanglement growth requires generic ("integrability breaking") interactions to be added to the pure transverse field Ising model.

cond-mat.dis-nn↗

arXiv2018

Hysteretic percolation from locally optimal individual decisions

The emergence of large-scale connectivity underlies the proper functioning of many networked systems, ranging from social networks and technological infrastructure to global trade networks. Percolation theory characterizes network formation following stochastic local rules, while optimization models of network formation assume a single controlling authority or one global objective function. In socio-economic networks, however, network formation is often driven by individual, locally optimal decisions. How such decisions impact connectivity is only poorly understood to date. Here, we study how large-scale connectivity emerges from decisions made by rational agents that individually minimize costs for satisfying their demand. We establish that the solution of the resulting nonlinear optimization model is exactly given by the final state of a local percolation process. This allows us to systematically analyze how locally optimal decisions on the micro-level define the structure of networks on the macroscopic scale.

physics.soc-ph↗

arXiv2018

Aging rate of spin glasses from simulations matches experiments

Experiments on spin glasses can now make precise measurements of the exponent $z(T)$ governing the growth of glassy domains, while our computational capabilities allow us to make quantitative predictions for experimental scales. However, experimental and numerical values for $z(T)$ have differed. We use new simulations on the Janus II computer to resolve this discrepancy, finding a time-dependent $z(T, t_w)$, which leads to the experimental value through mild extrapolations. Furthermore, theoretical insight is gained by studying a crossover between the $T = T_c$ and $T = 0$ fixed points.

cond-mat.dis-nn↗

arXiv2018

On the role of synaptic stochasticity in training low-precision neural networks

Stochasticity and limited precision of synaptic weights in neural network models are key aspects of both biological and hardware modeling of learning processes. Here we show that a neural network model with stochastic binary weights naturally gives prominence to exponentially rare dense regions of solutions with a number of desirable properties such as robustness and good generalization performance, while typical solutions are isolated and hard to find. Binary solutions of the standard perceptron problem are obtained from a simple gradient descent procedure on a set of real values parametrizing a probability distribution over the binary synapses. Both analytical and numerical results are presented. An algorithmic extension aimed at training discrete deep neural networks is also investigated.

cond-mat.dis-nn↗

arXiv2018

Critical Percolation Without Fine Tuning on the Surface of a Topological Superconductor

We present numerical evidence that most two-dimensional surface states of a bulk topological superconductor (TSC) sit at an integer quantum Hall plateau transition. We study TSC surface states in class CI with quenched disorder. Low-energy (finite-energy) surface states were expected to be critically delocalized (Anderson localized). We confirm the low-energy picture, but find instead that finite-energy states are also delocalized, with universal statistics that are independent of the TSC winding number, and consistent with the spin quantum Hall plateau transition (percolation).

cond-mat.dis-nn↗

arXiv2018

Translational and rotational dynamical heterogeneities in granular systems

We use X-ray tomography to investigate the translational and rotational dynamical heterogeneities of a three dimensional hard ellipsoids granular packing driven by oscillatory shear. We find that particles which translate quickly form clusters with a size distribution given by a power-law with an exponent that is independent of the strain amplitude. Identical behavior is found for particles that are translating slowly, rotating quickly, or rotating slowly. The geometrical properties of these four different types of clusters are the same as those of random clusters. Different cluster types are considerably correlated/anticorrelated, indicating a significant coupling between translational and rotational degrees of freedom. Surprisingly these clusters are formed already at time scales that are much shorter than the $α-$relaxation time, in stark contrast to the behavior found in glass-forming systems.

cond-mat.dis-nn↗

arXiv2017

Critical thermalization of a disordered dipolar spin system in diamond

Statistical mechanics underlies our understanding of macroscopic quantum systems. It is based on the assumption that out-of-equilibrium systems rapidly approach their equilibrium states, forgetting any information about their microscopic initial conditions. This fundamental paradigm is challenged by disordered systems, in which a slowdown or even absence of thermalization is expected. We report the observation of critical thermalization in a three dimensional ensemble of $\sim 10^6$ electronic spins coupled via dipolar interactions. By controlling the spin states of nitrogen vacancy color centers in diamond, we observe slow, sub-exponential relaxation dynamics and identify a regime of power-law decay with disorder-dependent exponents; this behavior is modified at late times owing to many-body interactions. These observations are quantitatively explained by a resonance counting theory that incorporates the effects of both disorder and interactions.

cond-mat.mes-hall↗

arXiv2018

Disorder engineering: From structural coloration to acoustic filters

We study Anderson localization of waves in a one dimensional disordered meta-material of bilayers comprising of thin fixed length scatterers placed randomly along a homogenous medium. As an interplay between order and disorder, we identify a new regime of strong disorder where the localization length becomes independent of the amount of disorder but depends on the frequency of the wave excitation and on the properties of the fixed length scatterer. As an example of a naturally occurring nearly one dimensional disordered bilayer, we calculate the wavelength dependent reflection spectrum for Koi fish using the experimentally measured parameters, and find that the main mechanisms for the emergence of their silver structural coloration can be explained through the phenomenon of Anderson localization of light in the regime of strong disorder discussed above. Finally, we show that by tuning the thickness of the fixed length scatterer, the above design principles could be used to engineer disordered meta-materials which selectively allows harmonics of a fundamental frequency to be transmitted in an effect which is similar to the insertion of a half wave cavity in a quarter wavelength stack. However, in contrast to the Lorentzian resonant peak of a half-wave cavity, we find that our disordered layer has a Gaussian lineshape whose width becomes narrower as the number of disordered layers is increased.

cond-mat.dis-nn↗

arXiv2021

Multifractality and self-averaging at the many-body localization transition

Finite-size effects have been a major and justifiable source of concern for studies of many-body localization, and several works have been dedicated to the subject. In this paper, however, we discuss yet another crucial problem that has received much less attention, that of the lack of self-averaging and the consequent danger of reducing the number of random realizations as the system size increases. By taking this into account and considering ensembles with a large number of samples for all system sizes analyzed, we find that the generalized dimensions of the eigenstates of the disordered Heisenberg spin-1/2 chain close to the transition point to localization are described remarkably well by an exact analytical expression derived for the non-interacting Fibonacci lattice, thus providing an additional tool for studies of many-body localization.

cond-mat.dis-nn↗

arXiv2013

Emergent percolation length and localization in random elastic networks

We study, theoretically and numerically, a minimal model for phonons in a disordered system. For sufficient disorder, the vibrational modes of this classical system can become Anderson localized, yet this problem has received significantly less attention than its electronic counterpart. We find rich behavior in the localization properties of the phonons as a function of the density, frequency and the spatial dimension. We use a percolation analysis to argue for a Debye spectrum at low frequencies for dimensions higher than one, and for a localization/delocalization transition (at a critical frequency) above two dimensions. We show that in contrast to the behavior in electronic systems, the transition exists for arbitrarily large disorder, albeit with an exponentially small critical frequency. The structure of the modes reflects a divergent percolation length that arises from the disorder in the springs without being explicitly present in the definition of our model. Within the percolation approach we calculate the speed-of-sound of the delocalized modes (phonons), which we corroborate with numerics. We find the critical frequency of the localization transition at a given density, and find good agreement of these predictions with numerical results using a recursive Green function method adapted for this problem. The connection of our results to recent experiments on amorphous solids are discussed.

cond-mat.dis-nn↗

arXiv2013

Mathematical Formulation of Multi-Layer Networks

A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is very rich. Achieving a deep understanding of such systems necessitates generalizing "traditional" network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multi-layer complex systems. In this paper, we introduce a tensorial framework to study multi-layer networks, and we discuss the generalization of several important network descriptors and dynamical processes --including degree centrality, clustering coefficients, eigenvector centrality, modularity, Von Neumann entropy, and diffusion-- for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multi-layer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.

physics.soc-ph↗