Condensed Matter

Beyond a critical disorder, two-dimensional (2D) superconductors become insulating. In this Superconductor-Insulator Transition (SIT), the nature of the insulator is still controversial. Here, we present an extensive experimental study on insulating Nb_{x}Si_{1-x} close to the SIT, as well as corresponding numerical simulations of the electrical conductivity. At low temperatures, we show that electronic transport is activated and dominated by charging energies. The sample thickness variation results in a large spread of activation temperatures, fine-tuned via disorder. We show numerically and experimentally that the localization length varies exponentially with thickness. At the lowest temperatures, overactivated behavior is observed in the vicinity of the SIT and the increase in the activation energy can be attributed to the superconducting gap. We derive a relation between the increase in activation energy and the temperature below which overactivated behavior is observed. This relation is verified by many different quasi-2D systems.

The complex dynamics of an increasing number of systems is attributed to the emergence of a rugged energy landscape with an exponential number of metastable states. To develop this picture into a predictive dynamical theory I discuss how to compute the exponentially small probability of a jump from one metastable state to another. This is expressed as a path integral that can be evaluated by saddle-point methods in mean-field models, leading to a boundary value problem. The resulting dynamical equations are solved numerically by means of a Newton-Krylov algorithm in the paradigmatic spherical p -spin glass model that is invoked in diverse contexts from supercooled liquids to machine-learning algorithms. I discuss the solutions in the asymptotic regime of large times and the physical implications on the nature of the ergodicity-restoring processes.

This paper is dedicated to the memory of Dietrich Stauffer, who was a pioneer in percolation theory and applications of it to problems of society, such as epidemiology. An epidemic is a percolation process gone out of control, that is, going beyond the critical transition threshold p c . Here we discuss how the threshold is related to the basic infectivity of neighbors R 0 , for trees (Bethe lattice), trees with triangular cliques, and in non-planar lattice percolation with extended-range connectivity. It is shown how having a smaller range of contacts increases the critical value of R 0 above the value R 0,c =1 appropriate for a tree, an infinite-range system or a large completely connected graph.

We develop a theory of percolation with plasticity systems (PWPs) rendering properties of interest for neuromorphic computing. Unlike the standard percolation between two large electrodes, they have multiple ( N≫1 ) interfaces and exponentially large number ( N! ) of conductive pathways between them. These pathways consist of non-ohmic random resistors that can undergo bias induced nonvolatile modifications (plasticity). The neuromorphic properties of PWPs include: multi-valued memory, high dimensionality and nonlinearity capable of transforming input data into spatiotemporal patterns, tunably fading memory ensuring outputs that depend more on recent inputs, and no need for massive interconnects. A few conceptual examples of functionality here are random number generation, matrix-vector multiplication, and associative memory. Understanding PWP topology, statistics, and operations opens a field of its own calling upon further theoretical and experimental insights.

Wavefront shaping (WFS) schemes for efficient energy deposition in weakly lossy targets is an ongoing challenge for many classical wave technologies relevant to next-generation telecommunications, long-range wireless power transfer, and electromagnetic warfare. In many circumstances these targets are embedded inside complicated enclosures which lack any type of (geometric or hidden) symmetry, such as complex networks, buildings, or vessels, where the hypersensitive nature of multiple interference paths challenges the viability of WFS protocols. We demonstrate the success of a new and general WFS scheme, based on coherent perfect absorption (CPA) electromagnetic protocols, by utilizing a network of coupled transmission lines with complex connectivity that enforces the absence of geometric symmetries. Our platform allows for control of the local losses inside the network and of the violation of time-reversal symmetry via a magnetic field; thus establishing CPA beyond its initial concept as the time-reversal of a laser cavity, while offering an opportunity for better insight into CPA formation via the implementation of semiclassical tools.

We consider the effects of on-site and hopping disorder on zero modes in the Su-Schrieffer-Heeger model. In the absence of disorder a domain wall gives rise to two chiral fractionalized bound states, one at the edge and one bound to the domain wall. On-site disorder breaks the chiral symmetry, in contrast to hopping disorder. By using the polarization we find that on-site disorder has little effect on the chiral nature of the bound states for weak to moderate disorder. We explore the behaviour of these bound states for strong disorder, contrasting on-site and hopping disorder and connect our results to the localization properties of the bound states and to recent experiments.

Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well known to be organized in hierarchical and modular way. While it is assumed that structural networks shape their functional counterparts, it is also hypothesized that alterations of brain dynamics come with transformations of functional connectivity. In this computational study, we introduce a novel methodology to monitor the persistence and breakdown of hierarchical order in functional networks, generated from computational models of activity spreading on both synthetic and real structural connectomes. We show that hierarchical connectivity appears in functional networks in a persistent way if the dynamics is set to be in the quasi-critical regime associated with optimal processing capabilities and normal brain function, while it breaks down in other (supercritical) dynamical regimes, often associated with pathological conditions. Our results offer important clues for the study of optimal neurocomputing architectures and processes, which are capable of controlling patterns of activity and information flow. We conclude that functional connectivity patterns achieve optimal balance between local specialized processing (i.e. segregation) and global integration by inheriting the hierarchical organization of the underlying structural architecture.

We examine the stability of marginally Anderson localized phase transitions between localized phases to the addition of many-body interactions, focusing in particular on the spin-glass to paramagnet transition in a disordered transverse field Ising model in one dimension. We find evidence for a perturbative instability of localization at finite energy densities once interactions are added, i.e. evidence for the relevance of interactions - in a renormalization group sense - to the non-interacting critical point governed by infinite randomness scaling. We introduce a novel diagnostic, the "susceptibility of entanglement", which allows us to perturbatively probe the effect of adding interactions on the entanglement properties of eigenstates, and helps us elucidate the resonant processes that can cause thermalization. The susceptibility serves as a much more sensitive probe, and its divergence can detect the perturbative beginnings of an incipient instability even in regimes and system sizes for which conventional diagnostics point towards localization. We expect this new measure to be of independent interest for analyzing the stability of localization in a variety of different settings.

Motivated by recent experimental observations [Phys. Rev. 96, 020407 (2017)] on hexagonal ferrites, we revisit the phase diagrams of diluted magnets close to the lattice percolation threshold. We perform large-scale Monte Carlo simulations of XY and Heisenberg models on both simple cubic lattices and lattices representing the crystal structure of the hexagonal ferrites. Close to the percolation threshold p c , we find that the magnetic ordering temperature T c depends on the dilution p via the power law T c ∼|p− p c | ϕ with exponent ϕ=1.09 , in agreement with classical percolation theory. However, this asymptotic critical region is very narrow, |p− p c |≲0.04 . Outside of it, the shape of the phase boundary is well described, over a wide range of dilutions, by a nonuniversal power law with an exponent somewhat below unity. Nonetheless, the percolation scenario does not reproduce the experimentally observed relation T c ∼( x c −x ) 2/3 in PbFe 12−x Ga x O 19 . We discuss the generality of our findings as well as implications for the physics of diluted hexagonal ferrites.

Recently, the use of neural quantum states for describing the ground state of many- and few-body problems has been gaining popularity because of their high expressivity and ability to handle intractably large Hilbert spaces. In particular, methods based on variational Monte Carlo have proven to be successful in describing the physics of bosonic systems such as the Bose-Hubbard (BH) model. However, this technique has not been systematically tested on the parameter space of the BH model, particularly at the boundary between the Mott insulator and superfluid phases. In this work, we evaluate the capabilities of variational Monte Carlo with a trial wavefunction given by a Restricted Boltzmann Machine to reproduce the quantum ground state of the BH model on several points of its parameter space. To benchmark the technique, we compare its results to the ground state found through exact diagonalization for small one-dimensional chains. In general, we find that the learned ground state correctly estimates many observables, reproducing to a high degree the phase diagram for the first Mott lobe and part of the second one. However, we find that the technique is challenged whenever the system transitions between excitation manifolds, as the ground state is not learned correctly at these boundaries. We improve the quality of the results produced by the technique by proposing a method to discard noisy probabilities learned in the ground state.