Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Ising and XY models with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are determined for systems starting separately from ordered and disordered initial states. The obtained values of the exponents are in a good agreement with results of the field-theoretic description of the critical behavior of these models in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.
We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, and to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.
We study the influence of scale-free correlated disorder on the metal-insulator transition in the Anderson model of localization. We use standard transfer matrix calculations and perform finite-size scaling of the largest inverse Lyapunov exponent to obtain the localization length for respective 3D tight-binding systems. The density of states is obtained from the full spectrum of eigenenergies of the Anderson Hamiltonian. We discuss the phase diagram of the metal-insulator transition and the influence of the correlated disorder on the critical exponents.
We study the band-centre anomaly in the one-dimensional Anderson model with weak correlated disorder. Our analysis is based on the Hamiltonian map approach; the correspondence between the discrete model and its continuous counterpart is discussed in detail. We obtain analytical expressions of the localisation length and of the invariant measure of the phase variable, valid for energies in a neighbourhood of the band centre. By applying these general results to specific forms of correlated disorder, we show how correlations can enhance or suppress the anomaly at the band centre.
We examine the transport of magnetic energy in a simplified model of a magnetic metamaterial, consisting of a one-dimensional array of split-ring resonators, in the presence of correlated disorder in the resonant frequencies. The computation of the average participation ratio (PR) reveals that on average, the modes for the correlated disorder system are less localized than in the uncorrelated case. The numerical computation of the mean square displacement of an initially localized magnetic excitation for the correlated case shows a substantial departure from the uncorrelated (Anderson-like) ca…
We analyse the thermal properties of a harmonic chain with weak correlated disorder. With the use of a perturbative approach we derive analytical expressions for the time-evolution of the chain temperature and of the heat flow when both ends of the chain are coupled to heat baths. Our analytical and numerical results demonstrate that specific long-range correlations of the isotopic disorder can suppress or enhance the vibrational modes in pre-defined frequency windows. In this way one can arrange a frequency-selective heat flow through disordered chains.
Comment on "Localization and the mobility edge in one-dimensional potentials with correlated disorder"
本文给出了一维（F）弱随机势的两点关联函数表示的波函数局域化长度方程。M.伊兹赖列夫和A. A. Krokhin，Phys. Rev. Lett. Vol.82，4062（1999））使用标准弱局域化理论重新推导。我提出了一个修改后的算法产生的任意相关的随机电位，并表明，数值计算的本地化长度在一个特定的相关的无序在1D，然后符合解析表达式，消除上述信件中指出的差异。
Tight-binding 1D random system with long-range correlations is studied numerically using the localisation criterium, which represents the number of sites, covered by the wave function. At low degrees of disorder the signs of a mobility edge, predicted in \cite{Izr}, were found. The possibility of exact mobility edge in the system under consideration is discussed.
We investigate a tight-binding electronic chain featuring diagonal and off-diagonal disorder, these being modelled through the long-range-correlated fractional Brownian motion. Particularly, by employing exact diagonalization methods, we evaluate how the eigenstate spectrum of the system and its related single-particle dynamics respond to both competing sources of disorder. Moreover, we report the possibility of carrying out efficient end-to-end quantum-state transfer protocols even in the presence of such generalized disorder due to the appearance of extended states around the middle of the b…
We study the critical behavior of the 2D $N$-color Ashkin-Teller model in the presence of random bond disorder whose correlations decays with the distance $r$ as a power-law $r^{-a}$. We consider the case when the spins of different colors sitting at the same site are coupled by the same bond and map this problem onto the 2D system of $N/2$ flavors of interacting Dirac fermions in the presence of correlated disorder. Using renormalization group we show that for $N=2$, a "weakly universal" scaling behavior at the continuous transition becomes universal with new critical exponents. For $N>2$, th…
Distribution of the transmission coefficient T of a long system with a correlated Gaussian disorder is studied analytically and numerically in terms of the generalized Lyapunov exponent (LE) and the cumulants of lnT. The effect of the disorder correlations on these quantities is considered in weak, moderate and strong disorder for different models of correlation. Scaling relations between the cumulants of lnT are obtained. The cumulants are treated analytically within the semiclassical approximation in strong disorder, and numerically for an arbitrary strength of the disorder. A small correlat…
We study the metal-insulator transition in a tight-binding one-dimensional (1D) model with long-range correlated disorder. In the case of diagonal disorder with site energy within $[-\frac{W}{2},\frac{W}{2}]$ and having a power-law spectral density $S(k)\propto k^{-α}$, we investigate the competition between the disorder and correlation. Using the transfer-matrix method and finite-size scaling analysis, we find out that there is a finite range of extended eigenstates for $α>2$, and the mobility edges are at $\pm E_{c}=\pm|2-W/2|$. Furthermore, we find the critical exponent $ν$ of localization …
We study the structure of the electronic states and the transport properties of a Kronig-Penney model with weak compositional and structural disorder. Using a perturbative approach we obtain an analytical expression for the localisation length which is valid for disorder with arbitrary correlations. We show how to generate disorder with self- and cross-correlations and we analyse both the known delocalisation effects of the long-range self-correlations and new effects produced by cross-correlations. We finally discuss how both kinds of correlations alter the transport properties in Kronig-Penn…
We numerically investigate dynamical property in the one-dimensional tight-binding model with long-range correlated disorder having power spectrum $1/f^α$ ($α:$spectrum exponent) generated by Fourier filtering method. For relatively small $α<α_c(=2)$ time-dependence of mean square displacement (MSD) of the initially localized wavepacket shows ballistic spread and localizes as time elapses. It is shown that $α-$dependence of the dynamical localization length (DLL) determined by the MSD exhibits a simple scaling law in the localization regime for the relatively weak disorder strength $W$. Furthe…
Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Heisenberg model with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are determined for systems starting from an ordered initial state. The obtained values of the exponents are in a good agreement with results of the field-theoretic description of the critical behavior of this model in the two-loop approximation.
We consider a one-dimensional quantum many-body system and investigate how the interplay between interaction and on-site disorder affects spatial localization and quantum correlations. The hopping amplitude is kept constant. To measure localization, we use the number of principal components (NPC), which quantifies the spreading of the system eigenstates over vectors of a given basis set. Quantum correlations are determined by a global entanglement measure $Q$, which quantifies the degree of entanglement of multipartite pure states. Our studies apply analogously to a one-dimensional system of i…
We investigate the spectral function of Bloch states in an one-dimensional tight-binding non-interacting chain with two different models of static correlated disorder, at zero temperature. We report numerical calculations of the single-particle spectral function based on the Kernel Polynomial Method, which has an $\mathcal{O}(N)$ computational complexity. These results are then confirmed by analytical calculations, where precise conditions were obtained for the appearance of a classical limit in a single-band lattice system. Spatial correlations in the disordered potential give rise to non-per…
We study transport properties of bulk-disordered quasi-one-dimensional (Q1D) wires paying main attention to the role of long-range correlations embedded into the disorder. First, we show that for stratified disorder for which the disorder is the same for all individual chains forming the Q1D wire, the transport properties can be analytically described provided the disorder is weak. When the disorder in every chain is not the same, however, has the same binary correlator, the general theory is absent. Thus, we consider the case when only one channel is open and all others are closed. For this s…
We introduce a new method, based on the recently developed random tensor theory, to study the p-spin glass model with non-Gaussian, correlated disorder. Using a suitable generalization of Gurau's theorem on the universality of the large N limit of the p-unitary ensemble of random tensors, we exhibit an infinite family of such non-Gaussian distributions which leads to same low temperature phase as the Gaussian distribution. While this result is easy to show (and well known) for uncorrelated disorder, its robustness with respect to strong quenched correlations is surprising. We show in detail ho…
We study the localization properties of normal modes in harmonic chains with mass and spring weak disorder. Using a perturbative approach, an expression for the localization length is obtained, which is valid for arbitrary correlations of the disorder, and for practically the whole frequency band. In addition, we show how to generate effective mobility edges by the use of disorder with long range self-correlations and cross-correlations. Finally, the transport of phonons is also analyzed showing effective transparent windows that can be manipulated through the disorder correlations even for re…
The disordered many-body systems can undergo a transition from the extended ensemble to a localized ensemble, known as many-body localization (MBL), which has been intensively explored in recent years. Nevertheless, the relation between Anderson localization (AL) and MBL is still elusive. Here we show that the MBL can be regarded as an infinite-dimensional AL with the correlated disorder in a virtual lattice. We demonstrate this idea using the disordered XXZ model, in which the excitation of $d$ spins over the fully polarized phase can be regarded as a single-particle model in a $d$ dimensiona…
The average energy of the Ising spin glass is known to have no singularity along a special line in the phase diagram although there exists a critical point on the line. This result on the model with uncorrelated disorder is generalized to the case with correlated disorder. For a class of correlations in disorder that suppress frustration, we show that the average energy in a subspace of the phase diagram is expressed as the expectation value of a local gauge variable of the $Z_2$ gauge Higgs model, from which we prove that the average energy has no singularity although the subspace is likely t…
Strongly correlated fermions in a crystal or in an optical lattice in the presence of binary alloy disorder are investigated. We employ the statistical dynamical mean-field theory, which incorporates both, local fluctuations due to disorder and local correlations due to interaction, to solve the Anderson-Hubbard model. Localization due to disorder is studied by means of the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram consisting of disordered correlated metal, Anderson-Mott insulator, and band insulator.
We evaluate the mean escape time of overdamped particles over potential barriers in short-correlated quenched Gaussian disorder potentials in one dimension at low temperature. The thermally activated escape is very sensitive to the form of the \emph{tail} of the potential barrier probability distribution. We evaluate this tail by using the optimal fluctuation method. For monotone decreasing autocovariances we reproduce the tail obtained by Lopatin and Vinokur (2001). However, for nonmonotonic autocovariances of the disorder potential we show that the tail changes. It is much higher when the di…
A Weyl semimetal denotes an electronic phase of solids in which two bands cross linearly. In this paper we study the effect of a spatially correlated disorder on such a phase. Using a renormalization group analysis, we show that in three dimensions, three scenarios are possible depending on the disorder correlations. A standard transition is recovered for short range correlations. For disorder decaying slower than $1/r^{2}$, the Weyl semimetal is unstable to any weak disorder and no transition persists. In between, a new phase transition occurs. This transition still separates a disordered met…
We investigate the outbreak of anomalous quantum wavefunction amplitudes in a one-dimensional tight-binding lattice featuring correlated diagonal disorder. Such rogue-wave-like behavior is fostered by a competition between localization and mobility. The effective correlation length of the disorder is ultimately responsible for bringing the local disorder strength to a minimum, fuelling the occurrence of extreme events of much higher amplitudes, specially when compared to the case of uncorrelated disorder. Our findings are valid for a class of discrete one-dimensional systems and reveal profoun…
Advances in material growth methods have renewed the interest in localization of one-dimensional systems in the presence of scale-free long-range correlated disorder potentials. We analyze the validity of single parameter scaling for the β-function away from the band center, in the presence of correlations. A renormalized disorder strength emerges reducing the regime of validity of the single parameter scaling hypothesis. Analysis of localization lengths and participation ratios leads to correlation dependent critical and fractal exponents, consistent with the extended Harris criterion.
We observe the emergence of a disorder-induced insulating state in a strongly interacting atomic Fermi gas trapped in an optical lattice. This closed quantum system free of a thermal reservoir realizes the disordered Fermi-Hubbard model, which is a minimal model for strongly correlated electronic solids. In measurements of disorder-induced localization obtained via mass transport, we detect interaction-driven delocalization and localization that persists as the temperature of the gas is raised. These behaviors are consistent with many-body localization, which is a novel paradigm for understand…
We study a canonical many-body-localized (MBL) system with power-law-correlated disorders: $s=\frac{1}{2}$ spin chain in a random magnetic field. The power-law-correlated disorder can control the critical regime between the MBL and thermal (ergodic) phases by varying its exponent, and it let us investigate the MBL transitions in detail. Static-eigenstate and dynamic properties of MBL are studied by numerical methods for systems with various long-range correlations. By using energy-resolved distribution of the participation ratio (PR) and calculating some physical quantities related to localiza…
We consider the $\pm J$ Ising model on a cubic lattice with a gauge-invariant disorder distribution. Disorder depends on a parameter $β_G$ that plays the role of a chemical potential for the amount of frustration. We study the model at a specific value of the disorder parameter $β_G$, where frustration shows long-range correlations. We characterize the universality class, obtaining accurate estimates of the critical exponents: $ν= 0.655(15)$ and $η_q = 1.05(5)$, where $η_q$ is the overlap susceptibility exponent.
Anderson localization has been a subject of intense studies for many years. In this context, we study numerically the influence of long-range correlated disorder on the localization behavior in one dimensional systems. We investigate the localization length and the density of states and compare our numerical results with analytical predictions. Specifically, we find two distinct characteristic behaviors in the vicinity of the band center and at the unperturbed band edge, respectively. Furthermore we address the effect of the intrinsic short-range correlations.
