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cond-mat.dis-nn

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preprint2016arXiv

Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach

We consider eigenvectors of the Hamiltonian $H_0$ perturbed by a generic perturbation $V$ modelled by a random matrix from the Gaussian Unitary Ensemble (GUE). Using the supersymmetry approach we derive analytical results for the statistics of the eigenvectors, which are non-perturbative in $V$ and valid for an arbitrary deterministic $H_0$. Further we generalise them to the case of a random $H_0$, focusing, in particular, on the Rosenzweig-Porter model. Our analytical predictions are confirmed by numerical simulations.

preprint2016arXiv

Effects of electron-impurity scattering on density of states in silicene: impurity bands and band-gap narrowing

Considering the interband correlation, we present a generalized multiple-scattering approach of Green's function to investigate the effects of electron-impurity scattering on the density of states in silicene. The reduction of energy gaps in the case of relatively high chemical potential and the transformation of split-off impurity bands into band tails for low chemical potential are found. The dependency of optical conductivity on the impurity concentration is also discussed for frequency within the terahertz regime.

preprint2016arXiv

Chiral Floquet Phases of Many-body Localized Bosons

We construct and classify chiral topological phases in driven (Floquet) systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with chiral edges, which in the presence of many-body localization (MBL) in the bulk are argued to lead to stable chiral phases. These chiral phases do not require any symmetry, and in fact owe their existence to the absence of energy conservation in driven systems. Surprisingly, we show that they are classified by a quantized many-body index, which is well defined for any MBL Floquet system. The value of this index, which is always the logarithm of a positive rational number, can be interpreted as the entropy per Floquet cycle pumped along the edge, formalizing the notion of quantum-information flow. We explicitly compute this index for specific models, and show that the nontrivial topology leads to edge thermalization, which provides an interesting link between bulk topology and chaos at the edge. We also discuss chiral Floquet phases in interacting fermionic systems and their relation to chiral bosonic phases.

preprint2016arXiv

Itinerant conductance in fuse-antifuse networks

We report on a novel dynamic phase in electrical networks, in which current channels perpetually change in time. This occurs when the individual elements of the network are fuse-antifuse devices, namely, become insulators within a certain finite interval of local applied voltages. As a consequence, the macroscopic current exhibits temporal fluctuations which increase with system size. We determine the conditions under which this exotic situation appears by establishing a phase diagram as a function of the applied field and the size of the insulating window. Besides its obvious application as a versatile electronic device, due to its rich variety of behaviors, this network model provides a possible description for particle-laden flow through porous media leading to dynamical clogging and reopening of the local channels in the pore space.

preprint2016arXiv

Generalized Multiband Typical Medium Dynamical Cluster Approximation: Application to (Ga,Mn)N

We generalize the multiband typical medium dynamical cluster approximation and the formalism introduced by Blackman, Esterling and Berk so that it can deal with localization in multiband disordered systems with both diagonal and off-diagonal disorder with complicated potentials. We also introduce a new ansatz for the angle resolved typical density of states that greatly improves the numerical stability of the method while preserving the independence of scattering events at different frequencies. Starting from the first-principles effective Hamiltonian, we apply this method to the diluted magnetic semiconductor Ga$_{1-x}$Mn$_x$N, and find the impurity band is completely localized for Mn concentrations $x<0.03$ while for $0.03 <x<0.10$ the impurity band has delocalized states but the chemical potential resides at or above the mobility edge. So, the system is always insulating within the experimental compositional limit ($x\approx 0.10$) due to Anderson localization. However, for $0.03 <x<0.10$ hole doping could make the system metallic allowing double exchange mediated, or enhanced, ferromagnetism. The developed method is expected to have a large impact on first-principles studies of

preprint2016arXiv

Transport and localization of waves in ladder-shaped lattices with locally $\mathcal{PT}$-symmetric potentials

We study numerically the transport and localization properties of waves in ordered and disordered ladder-shaped lattices with local $\mathcal{PT}$ symmetry. Using a transfer matrix method, we calculate the transmittance and the reflectance for the individual channels and the Lyapunov exponent for the whole system. In the absence of disorder, we find that when the gain/loss parameter $ρ$ is smaller than the interchain coupling parameter $t_{v}$, the transmittance and the reflectance are periodic functions of the system size, whereas when $ρ$ is larger than $t_{v}$, the transmittance is found to be an exponentially-decaying function while the reflectance attains a saturation value in the thermodynamic limit. For a fixed system size, there appear perfect transmission resonances in each individual channel at several values of the gain/loss strength smaller than $t_{v}$. A singular behavior of the transmittance is also found to appear at various values of $ρ$ for a given system size. When disorder is inserted into the on-site potentials, these behaviors are changed substantially due to the interplay between disorder and the gain/loss effect. When $ρ$ is smaller than $t_{v}$, we find tha

preprint2016arXiv

Percolation in Finite Matching Lattices

We derive an exact, simple relation between the average number of clusters and the wrapping probabilities for two-dimensional percolation. The relation holds for periodic lattices of any size. It generalizes a classical result of Sykes and Essam and it can be used to find exact or very accurate approximations of the critical density. The criterion that follows is related to the criterion Scullard and Jacobsen use to find precise approximate thresholds, and our work provides a new perspective on their approach.

preprint2016arXiv

The random anisotropy model revisited

We revisit the thermodynamic behavior of the random-anisotropy O($N$) model by investigating its large-$N$ limit. We focus on the system at zero temperature where the mean-field-like artifacts of the large-$N$ limit are less severe. We analyze the connection between the description in terms of self-consistent Schwinger-Dyson equations and the functional renormalization group. We provide a unified description of the phase diagram and critical behavior of the model and clarify the nature of the possible "glassy" phases. Finally we discuss the implications of our findings for the finite-$N$ and finite-temperature systems.

preprint2016arXiv

Phase diagram of matrix compressed sensing

In the problem of matrix compressed sensing we aim to recover a low-rank matrix from few of its element-wise linear projections. In this contribution we analyze the asymptotic performance of a Bayes-optimal inference procedure for a model where the matrix to be recovered is a product of random matrices. The results that we obtain using the replica method describe the state evolution of the recently introduced P-BiG-AMP algorithm. We show the existence of different types of phase transitions, their implications for the solvability of the problem, and we compare the results of the theoretical analysis to the performance reached by P-BiG-AMP. Remarkably the asymptotic replica equations for matrix compressed sensing are the same as those for a related but formally different problem of matrix factorization.

preprint2016arXiv

Replica approach to mean-variance portfolio optimization

We consider the problem of mean-variance portfolio optimization for a generic covariance matrix subject to the budget constraint and the constraint for the expected return, with the application of the replica method borrowed from the statistical physics of disordered systems. We find that the replica symmetry of the solution does not need to be assumed, but emerges as the unique solution of the optimization problem. We also check the stability of this solution and find that the eigenvalues of the Hessian are positive for $r=N/T<1$, where $N$ is the dimension of the portfolio and $T$ the length of the time series used to estimate the covariance matrix. At the critical point $r=1$ a phase transition is taking place. The out of sample estimation error blows up at this point as $1/(1-r)$, independently of the covariance matrix or the expected return, displaying the universality not only of the critical index, but also the critical point. As a conspicuous illustration of the dangers of in-sample estimates, the optimal in-sample variance is found to vanish at the critical point inversely proportional to the divergent estimation error.

preprint2017arXiv

Critical assessment of the equilibrium melting-based, energy distribution theory of supercooled liquids and application to jammed systems

Despite decades of intense study, the mechanisms underlying the extraordinary dynamics of supercooled liquids as they approach the glass transition remain, at best, mis-characterized, and at worst, misunderstood. A long standing endeavor is to understand the remarkable increase of the viscosity with supercooling. Recently, a new theory of supercooled liquids has been proposed that starts from first principles, using elementary statistical mechanics arguments, to derive a form for the viscosity that contains only a single fitting parameter in its simplest form. In this we demonstrate that this exact same form may be derived from a different starting point, and then critically examine its performance. In the process we find that functional form proposed fits the viscosity data of a diverse group of 45 liquids exceptionally well over a wide temperature range, and uncover a number of interesting correlations of the single parameter with various thermodynamic quantities, ultimately allowing for the prediction of low temperature viscosity from high temperature data. Additionally, we find that similar physical reasoning can be used to derive a similar, single parameter form for the viscos

preprint2013arXiv

Parallel Tempering Simulation of the three-dimensional Edwards-Anderson Model with Compact Asynchronous Multispin Coding on GPU

Monte Carlo simulations of the Ising model play an important role in the field of computational statistical physics, and they have revealed many properties of the model over the past few decades. However, the effect of frustration due to random disorder, in particular the possible spin glass phase, remains a crucial but poorly understood problem. One of the obstacles in the Monte Carlo simulation of random frustrated systems is their long relaxation time making an efficient parallel implementation on state-of-the-art computation platforms highly desirable. The Graphics Processing Unit (GPU) is such a platform that provides an opportunity to significantly enhance the computational performance and thus gain new insight into this problem. In this paper, we present optimization and tuning approaches for the CUDA implementation of the spin glass simulation on GPUs. We discuss the integration of various design alternatives, such as GPU kernel construction with minimal communication, memory tiling, and look-up tables. We present a binary data format, Compact Asynchronous Multispin Coding (CAMSC), which provides an additional $28.4\%$ speedup compared with the traditionally used Asynchrono

preprint2016arXiv

Extensive degeneracy, Coulomb phase and magnetic monopoles in an artificial realization of the square ice model

Artificial spin ice systems have been introduced as a possible mean to investigate frustration effects in a well-controlled manner by fabricating lithographically-patterned two-dimensional arrangements of interacting magnetic nanostructures. This approach offers the opportunity to visualize unconventional states of matter, directly in real space, and triggered a wealth of studies at the frontier between nanomagnetism, statistical thermodynamics and condensed matter physics. Despite the strong efforts made these last ten years to provide an artificial realization of the celebrated square ice model, no simple geometry based on arrays of nanomagnets succeeded to capture the macroscopically degenerate ground state manifold of the corresponding model. Instead, in all works reported so far, square lattices of nanomagnets are characterized by a magnetically ordered ground state consisting of local flux-closure configurations with alternating chirality. Here, we show experimentally and theoretically, that all the characteristics of the square ice model can be observed if the artificial square lattice is properly designed. The spin configurations we image after demagnetizing our arrays reve

preprint2016arXiv

Exact solution for a random walk in a time-dependent 1D random environment: the point-to-point Beta polymer

We consider the Beta polymer, an exactly solvable model of directed polymer on the square lattice, introduced by Barraquand and Corwin. We study the statistical properties of its point to point partition sum. The problem is equivalent to a model of a random walk in a time-dependent (and in general biased) 1D random environment. In this formulation, we study the sample to sample fluctuations of the transition probability distribution function (PDF) of the random walk. Using the Bethe ansatz we obtain exact formulas for the integer moments, and Fredholm determinant formulas for the Laplace transform of the directed polymer partition sum/random walk transition probability. The asymptotic analysis of these formulas at large time $t$ is performed both (i) in a diffusive vicinity, $x \sim t^{1/2}$, of the optimal direction (in space-time) chosen by the random walk, where the fluctuations of the PDF are found to be Gamma distributed; (ii) in the large deviations regime, $x \sim t$, of the random walk, where the fluctuations of the logarithm of the PDF are found to grow with time as $t^{1/3}$ and to be distributed according to the Tracy-Widom GUE distribution. Our exact results complement

preprint2015arXiv

Narayanaswamy's 1971 aging theory and material time

The Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem is used to derive Narayanaswamy's phenomenological theory of physical aging, in which this highly nonlinear phenomenon is described by a linear material-time convolution integral. A characteristic property of the Narayanaswamy aging description is material-time translational invariance, which is here taken as the basic assumption of the derivation. It is shown that only one possible definition of the material time obeys this invariance, namely the square of the distance travelled from a configuration of the system far back in time. The paper concludes with suggestions for computer simulations that test for consequences of material-time translational invariance. One of these is the "unique-triangles property" according to which any three points on the system's path form a triangle such that two side lengths determine the third; this is equivalent to the well-known triangular relation for time-autocorrelation functions of aging spin glasses [L. F. Cugliandolo and J. Kurchan, J. Phys. A: Math. Gen. 27, 5749 (1994)]. The unique-triangles property implies a simple geometric interpretation of out-of-equilibriu

preprint2016arXiv

Statistical mechanics of clonal expansion in lymphocyte networks modelled with slow and fast variables

We study the Langevin dynamics of the adaptive immune system, modelled by a lymphocyte network in which the B cells are interacting with the T cells and antigen. We assume that B clones and T clones are evolving in different thermal noise environments and on different timescales. We derive stationary distributions and use statistical mechanics to study clonal expansion of B clones in this model when the B and T clone sizes are assumed to be the slow and fast variables respectively and vice versa. We derive distributions of B clone sizes and use general properties of ferromagnetic systems to predict characteristics of these distributions, such as the average B cell concentration, in some regimes where T cells can be modelled as binary variables. This analysis is independent of network topologies and its results are qualitatively consistent with experimental observations. In order to obtain full distributions we assume that the network topologies are random and locally equivalent to trees. The latter allows us to employ the Bethe-Peierls approach and to develop a theoretical framework which can be used to predict the distributions of B clone sizes. As an example we use this theory to

preprint2016arXiv

Finite size scaling for the Many-Body-Localization Transition : finite-size-pseudo-critical points of individual eigenstates

To understand the finite-size-scaling properties of phases transitions in classical and quantum models in the presence of quenched disorder, it has proven to be fruitful to introduce the notion of a finite-size-pseudo-critical point in each disordered sample and to analyze its sample-to-sample fluctuations as a function of the size. For the Many-Body-Localization transition, where very strong eigenstate-to-eigenstate fluctuations have been numerically reported even within a given disordered sample at a given energy density [X. Yu, D. J. Luitz, B. K. Clark, arxiv:1606.01260 and V. Khemani, S. P. Lim, D. N. Sheng, D. A. Huse,arxiv:1607.05756], it seems thus useful to introduce the notion of a finite-size-pseudo-critical point for each individual eigenstate and to study its eigenstate-to-eigenstate fluctuations governed by the correlation length exponent $ν$. The scaling properties of critical eigenstates are also expected to appear much more clearly if one considers each eigenstate at its finite-size-pseudo-critical point, where it is 'truly critical', while standard averages over eigenstates and samples in the critical region actually see a mixture of states that are effecti

preprint2017arXiv

Sparse model selection in the highly under-sampled regime

We propose a method for recovering the structure of a sparse undirected graphical model when very few samples are available. The method decides about the presence or absence of bonds between pairs of variable by considering one pair at a time and using a closed form formula, analytically derived by calculating the posterior probability for every possible model explaining a two body system using Jeffreys prior. The approach does not rely on the optimisation of any cost functions and consequently is much faster than existing algorithms. Despite this time and computational advantage, numerical results show that for several sparse topologies the algorithm is comparable to the best existing algorithms, and is more accurate in the presence of hidden variables. We apply this approach to the analysis of US stock market data and to neural data, in order to show its efficiency in recovering robust statistical dependencies in real data with non stationary correlations in time and space.

preprint2016arXiv

Anderson localization on random regular graphs

A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity. In certain sense, the RRG ensemble can be seen as infinite-dimensional ($d\to\infty$) cousin of Anderson model in d dimensions. We focus on the delocalized side of the transition and stress the importance of finite-size effects. We show that the data can be interpreted in terms of the finite-size crossover from small ($N\ll N_c$) to large ($N\gg N_c$) system, where $N_c$ is the correlation volume diverging exponentially at the transition. A distinct feature of this crossover is a nonmonotonicity of the spectral and wavefunction statistics, which is related to properties of the critical phase in the studied model and renders the finite-size analysis highly non-trivial. Our results support an analytical prediction that states in the delocalized phase (and at $N\gg N_c$) are ergodic in the sense that their inverse participation ratio scales as $1/N$.

preprint2016arXiv

On the possibility of many-body localization in a doped Mott insulator

Many-body localization (MBL) is currently a hot issue of interacting systems, in which quantum mechanics overcomes thermalization of statistical mechanics. Like Anderson localization of non-interacting electrons, disorders are usually crucial in engineering the quantum interference in MBL. For translation invariant systems, however, the breakdown of eigenstate thermalization hypothesis due to a \emph{pure} many-body quantum effect is still unclear. Here we demonstrate a possible MBL phenomenon without disorder, which emerges in a lightly doped Hubbard model with very strong interaction. By means of density matrix renormalization group numerical calculation on a two-leg ladder, we show that whereas a single hole can induce a very heavy Nagaoka polaron, two or more holes will form bound pair/droplets which are all localized excitations with flat bands at low energy densities. Consequently, MBL eigenstates of finite energy density can be constructed as composed of these localized droplets spatially separated. We further identify the underlying mechanism for this MBL as due to a novel `Berry phase' of the doped Mott insulator, and show that by turning off this Berry phase either by

preprint2016arXiv

Comment on "Critical point scaling of Ising spin glasses in a magnetic field" by J. Yeo and M.A. Moore

In a section of a recent publication, [J. Yeo and M.A. Moore, Phys. Rev. B 91, 104432 (2015)], the authors discuss some of the arguments in the paper by Parisi and Temesvári [Nuclear Physics B 858, 293 (2012)]. In this comment, it is shown how these arguments are misinterpreted, and the existence of the Almeida-Thouless transition in the upper critical dimension 6 reasserted.

preprint2016arXiv

On the disorder-driven quantum transition in three-dimensional relativistic metals

The Weyl semimetals are topologically protected from a gap opening against weak disorder in three dimensions. However, a strong disorder drives this relativistic semimetal through a quantum transition towards a diffusive metallic phase characterized by a finite density of states at the band crossing. This transition is usually described by a perturbative renormalization group in $d=2+\varepsilon$ of a $U(N)$ Gross-Neveu model in the limit $N \to 0$. Unfortunately, this model is not multiplicatively renormalizable in $2+\varepsilon$ dimensions: An infinite number of relevant operators are required to describe the critical behavior. Hence its use in a quantitative description of the transition beyond one-loop is at least questionable. We propose an alternative route, building on the correspondence between the Gross-Neveu and Gross-Neveu-Yukawa models developed in the context of high energy physics. It results in a model of Weyl fermions with a random non-Gaussian imaginary potential which allows one to study the critical properties of the transition within a $d=4-\varepsilon$ expansion. We also discuss the characterization of the transition by the multifractal spectrum of wave functi

preprint2016arXiv

Comment on "Crossover of collective modes and positive sound dispersion in supercritical state"

We comment on an expression for positive sound dispersion (PSD) in fluids and analysis of PSD from molecular dynamics simulations reported in the Letter by Fomin et al (J.Phys.:Condens.Matt. v.28, 43LT01, 2016)

preprint2016arXiv

Mean-Field Monomer-Dimer models. A review

A collection of rigorous results for a class of mean-field monomer-dimer models is presented. It includes a Gaussian representation for the partition function that is shown to considerably simplify the proofs. The solutions of the quenched diluted case and the random monomer case are explained. The presence of the attractive component of the Van der Waals potential is considered and the coexistence phase coexistence transition analysed. In particular the breakdown of the central limit theorem is illustrated at the critical point where a non Gaussian, quartic exponential distribution is found for the number of monomers centered and rescaled with the volume to the power 3/4.

1027 works