Condensed Matter

We analyze the random sequential dynamics of a message passing algorithm for Ising models with random interactions in the large system limit. We derive exact results for the two-time correlation functions and the speed of convergence. The {\em de Almedia-Thouless} stability criterion of the static problem is found to be necessary and sufficient for the global convergence of the random sequential dynamics.

We study excitations of atomic vibrations in the reciprocal space for amorphous solids. There are two kinds of excitations we obtained, collective excitation and local excitation. The collective excitation is the collective vibration of atoms in the amorphous solids while the local excitation is stimulated locally by a single atom vibrating in the solids. We introduce a continuous wave vector for the study and transform the equations of atomic vibrations from the real space to the reciprocal space. We take the amorphous silicon as an example and calculate the structures of the excitations in the reciprocal space. Results show that an excitation is a wave packet composed of a collection of plane waves. We also find a periodical structure in the reciprocal space for the collective excitation with longitudinal vibrations, which is originated from the local order of the structure in the real space of the amorphous solid.

Among the models of disordered conduction and localization, models with N orbitals per site are attractive both for their mathematical tractability and for their physical realization in coupled disordered grains. However Wegner proved that there is no Anderson transition and no localized phase in the N?��? limit, if the hopping constant K is kept fixed. Here we show that the localized phase is preserved in a different limit where N is taken to infinity and the hopping K is simultaneously adjusted to keep NK constant. We support this conclusion with two arguments. The first is numerical computations of the localization length showing that in the N?��? limit the site-diagonal-disorder model possesses a localized phase if NK is kept constant, but does not possess that phase if K is fixed. The second argument is a detailed analysis of the energy and length scales in a functional integral representation of the gauge invariant model. The analysis shows that in the K fixed limit the functional integral's spins do not exhibit long distance fluctuations, i.e. such fluctuations are massive and therefore decay exponentially, which signals conduction. In contrast the NK fixed limit preserves the massless character of certain spin fluctuations, allowing them to fluctuate over long distance scales and cause Anderson localization.

We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is not the case for the more commonly studied generalization of percolation to multiplex networks, the mutually connected clusters, which requires an interconnecting path within each layer between any two vertices in the giant mutually connected component. We study the emergence of a giant connected component of active nodes under the weak percolation rule, finding several non-typical phenomena. In two layers, the giant component emerges with a continuos phase transition, but with quadratic growth above the critical threshold. In three or more layers, a discontinuous hybrid transition occurs, similar to that found in the giant mutually connected component. In networks with asymptotically powerlaw degree distributions, defined by the decay exponent γ , the discontinuity vanishes but at γ=1.5 in three layers, more generally at γ=1+1/(M−1) in M layers.

Statistical spin dynamics plays a key role to understand the working principle for novel optical Ising machines. Here we propose the gauge transformations for spatial photonic Ising machine, where a single spatial phase modulator simultaneously encodes spin configurations and programs interaction strengths. Thanks to gauge transformation, we experimentally evaluate the phase diagram of high-dimensional spin-glass equilibrium system with 100 fully-connected spins. We observe the presence of paramagnetic, ferromagnetic as well as spin-glass phases and determine the critical temperature T c and the critical probability p c of phase transitions, which agree well with the mean-field theory predictions. Thus the approximation of the mean-field model is experimentally validated in the spatial photonic Ising machine. Furthermore, we discuss the phase transition in parallel with solving combinatorial optimization problems during the cooling process and identify that the spatial photonic Ising machine is robust with sufficient many-spin interactions, even when the system is associated with the optical aberrations and the measurement uncertainty.

We present wave transport experiments in hyperuniform disordered arrays of cylinders with high dielectric permittivity. Using microwaves, we show that the same material can display transparency, photon diffusion, Anderson localization, or a full band gap, depending on the frequency ν of the electromagnetic wave. Interestingly, we find a second weaker band gap, which appears to be related to the second peak of the structure factor. Our results emphasize the importance of spatial correlations on different length scales for the formation of photonic band gaps.

Synchronization is an important collective phenomenon in interacting oscillatory agents. Many functional features of the brain are related to synchronization of neurons. The type of synchronization transition that may occur (explosive vs. continuous) has been the focus of intense attention in recent years, mostly in the context of phase oscillator models for which collective behavior is independent of the mean-value of natural frequency. However, synchronization properties of biologically-motivated neural models depend on the firing frequencies. In this study we report a systematic study of gamma-band synchronization in spiking Hodgkin-Huxley neurons which interact via electrical or chemical synapses. We use various network models in order to define the connectivity matrix. We find that the underlying mechanisms and types of synchronization transitions in gamma-band differs from beta-band. In gamma-band, network regularity suppresses transition while randomness promotes a continuous transition. Heterogeneity in the underlying topology does not lead to any change in the order of transition, however, correlation between number of synapses and frequency of a neuron will lead to explosive synchronization in heterogenous networks with electrical synapses. Furthermore, small-world networks modeling a fine balance between clustering and randomness (as in the cortex), lead to explosive synchronization with electrical synapses, but a smooth transition in the case of chemical synapses. We also find that hierarchical modular networks, such as the connectome, lead to frustrated transitions. We explain our results based on various properties of the network, paying particular attention to the competition between clustering and long-range synapses.

In this work, we address the question whether a sufficiently deep quantum neural network can approximate a target function as accurate as possible. We start with simple but typical physical situations that the target functions are physical observables, and then we extend our discussion to situations that the learning targets are not directly physical observables, but can be expressed as physical observables in an enlarged Hilbert space with multiple replicas, such as the Loshimidt echo and the Renyi entropy. The main finding is that an accurate approximation is possible only when the input wave functions in the dataset do not exhaust the entire Hilbert space that the quantum circuit acts on, and more precisely, the Hilbert space dimension of the former has to be less than half of the Hilbert space dimension of the latter. In some cases, this requirement can be satisfied automatically because of the intrinsic properties of the dataset, for instance, when the input wave function has to be symmetric between different replicas. And if this requirement cannot be satisfied by the dataset, we show that the expressivity capabilities can be restored by adding one ancillary qubit where the wave function is always fixed at input. Our studies point toward establishing a quantum neural network analogy of the universal approximation theorem that lays the foundation for expressivity of classical neural networks.

We explore thermalization and quantum dynamics in a one-dimensional disordered SU(2)-symmetric Floquet model, where a many-body localized phase is prohibited by the non-abelian symmetry. Despite the absence of localization, we find an extended nonergodic regime at strong disorder where the system exhibits nonthermal behaviors. In the strong disorder regime, the level spacing statistics exhibit neither a Wigner-Dyson nor a Poisson distribution, and the spectral form factor does not show a linear-in-time growth at early times characteristic of random matrix theory. The average entanglement entropy of the Floquet eigenstates is subthermal, although violating an area-law scaling with system sizes. We further compute the expectation value of local observables and find strong deviations from the eigenstate thermalization hypothesis. The infinite temperature spin autocorrelation function decays at long times as t −β with β<0.5 , indicating subdiffusive transport at strong disorders.

One challenge of studying the many-body localization transition is defining the length scale that diverges upon the transition to the ergodic phase. In this manuscript we explore the localization properties of a ring with onsite disorder subject to an imaginary magnetic flux. We connect the imaginary flux which delocalizes single-particle orbitals of an Anderson-localized ring with the localization length of an open chain. We thus identify the delocalizing imaginary flux per site with the inverse localization length. We put this intuition to use by exploring the phase diagram of a disordered interacting chain, and find that the inverse imaginary flux per bond provides an accessible description of the transition and its diverging localization length.