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Imre Varga

Publications and source records attributed to Imre Varga.

At least 19 recordsLinked to original sources
arXiv2026

Quantum and classical entropic complexity of the thermal state: coherence, decoherence, and the ergodic-to-localized crossover in random-matrix and many-body models

Does thermal averaging preserve signatures of eigenstate complexity? We study the entropic complexity C = S_1 - S_2 (Shannon minus second-order Renyi entropy) across the ergodic-to-localized crossover of three disordered models: the Rosenzweig-Porter (RP) ensemble, the power-law banded random matrix (PLBRM) ensemble, and the random-field Heisenberg chain. We compare a wavefunction-level quantity C_eig to the complexity of the thermal (Gibbs) state before and after pointer-basis dephasing, via the trace (C_tr) and diagonal (C_diag) complexities. The answer is mostly no: thermal averaging strongly suppresses, but does not eliminate, eigenstate-complexity signatures. C_eig develops a pronounced mid-phase maximum in RP and, at matching fractal dimension, in the structurally independent PLBRM model; a high-statistics scan resolves a weak (about 10%) but reproducible thermal shadow of this peak in the thermal diagonal complexity. This feature is confined to the two random-matrix models; in the Heisenberg chain the eigenstate complexity instead peaks at the many-body localization transition. A second, genuinely thermal feature, an edge just inside the ergodic phase, has no eigenstate counterpart and, in PLBRM, recedes with system size. Both features are tracked by scale-invariant crossover indicators: the log-ratio of the trace and diagonal crossover temperatures, which vanishes upon localization, and the relative entropy of coherence. Entropic complexity thus cleanly separates thermal-state and eigenstate physics: a sharp wavefunction-level feature, reproducible across unrelated random-matrix constructions, leaves only a faint, structurally distinct imprint on thermal observables.

cond-mat.dis-nn↗
arXiv2025

Complexity in multi-qubit and many-body systems

Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the divergence between the Shannon or von Neumann entropy of the computational basis distribution and the second-order Renyi entropy. This quantity has already been used earlier termed as structural entropy and it is particularly powerful as the Renyi entropy is directly related to state purity, linear entropy, and the inverse participation ratio, providing a clear physical grounding. While other Renyi orders could be used, the second order offers a deep and established connection to these key physical quantities. We first validate the measure in canonical noise channels, showing it peaks at the boundary between quantum and classical regimes. We then demonstrate its power in many-body physics. For systems exhibiting a many-body localization transition - including deformed random matrix ensembles and a disordered Heisenberg spin chain - the complexity measure reliably signals the crossover from integrable/localized to quantum-chaotic/ergodic phases. Crucially, the maximum complexity occurs in the non-ergodic yet extended states at the transition, precisely capturing the critical region where the system is neither fully localized nor thermalized. Furthermore, within the chaotic phase, the measure correlates with the survival probability of local excitations, revealing a spectrum of thermalization properties. Our results establish that the entropic complexity is a simple, versatile, and effective probe for identifying nontrivial quantum regimes and transitions giving a new and alternative insight into such systems.

quant-ph↗
arXiv2024

Complexity of two-level systems

Complexity of two-level systems, e.g. spins, qubits, magnetic moments etc, are analysed based on the so-called correlational entropy in the case of pure quantum systems and the thermal entropy in case of thermal equilibrium that are suitable quantities essentially free from basis dependence. The complexity is defined as the difference between the Shannon-entropy and the second order R\'enyi-entropy, where the latter is connected to the traditional participation measure or purity. It is shown that the system attains maximal complexity for special choice of control parameters, i.e. strength of disorder either in the presence of noise of the energy states or the presence of disorder in the off diagonal coupling. It is shown that such a noise or disorder dependence provides a basis free analysis and gives meaningful insights. We also look at similar entropic complexity of spins in thermal equilibrium for a paramagnet at finite temperature, $T$ and magnetic field $B$, as well as the case of an Ising model in the mean-field approximation. As a result all examples provide important evidence that the investigation of the entropic complexity parameters help to get deeper understanding in the behavior of these systems.

quant-ph↗
arXiv2015

Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions

The disorder induced metal--insulator transition is investigated in a three-dimensional simple cubic lattice and compared for the presence and absence of time-reversal and spin-rotational symmetry, i.e. in the three conventional symmetry classes. Large scale numerical simulations have been performed on systems with linear sizes up to $L=100$ in order to obtain eigenstates at the band center, $E=0$. The multifractal dimensions, exponents $D_q$ and $α_q$, have been determined in the range of $-1\leq q\leq 2$. The finite-size scaling of the generalized multifractal exponents provide the critical exponents for the different symmetry classes in accordance with values known from the literature based on high precision transfer matrix techniques. The multifractal exponents of the different symmetry classes provide further characterization of the Anderson transition, which was missing from the literature so far.

cond-mat.dis-nn↗
arXiv2015

Emergence of energy dependence in the fragmentation of heterogeneous materials

The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of universality depending mainly on the dimensionality and on the brittle-ductile mechanical response of the system. Recently, experiments and computer simulations have reported an energy dependence of the exponent increasing with the imparted energy. These novel findings question the phase transition picture of fragmentation phenomena, and have also practical importance for industrial applications. Based on large scale computer simulations here we uncover a robust mechanism which leads to the emergence of energy dependence in fragmentation processes resolving controversial issues on the problem: studying the impact induced breakup of plate-like objects with varying thickness in three dimensions we show that energy dependence occurs when a lower dimensional fragmenting object is embedded into a higher dimensional space. The reason is an underlying transition between two distinct fragmentation mechanisms controlled by the impact velocity at low plate thicknesses, while it is hindered for three-dimensional bulk systems. The mass distributions of the subsets of fragments dominated by the two cracking mechanisms proved to have an astonishing robustness at all plate thicknesses, which implies that the non-universality of the complete mass distribution is the consequence of blending the contributions of universal partial processes.

cond-mat.dis-nn↗
arXiv2014

Dirac eigenmodes at the QCD Anderson transition

Recently we found an Anderson-type localization-delocalization transition in the QCD Dirac spectrum at high temperature. Using spectral statistics we obtained a critical exponent compatible with that of the corresponding Anderson model. Here we study the spatial structure of the eigenmodes both in the localized and the transition region. Based on previous studies in the Anderson model, at the critical point, the eigenmodes are expected to have a scale invariant multifractal structure. We verify the scale invariance of Dirac eigenmodes at the critical point.

hep-lat↗
arXiv2014

Quantum percolation transition in 3d: density of states, finite size scaling and multifractality

The phase diagram of the metal-insulator transition in a three dimensional quantum percolation problem is investigated numerically based on the multifractal analysis of the eigenstates. The large scale numerical simulation has been performed on systems with linear sizes up to $L=140$. The multifractal dimensions, exponents $D_q$ and $α_q$, have been determined in the range of $0\leq q\leq 1$. Our results confirm that this problem belongs to the same universality class as the three dimensional Anderson model, the critical exponent of the localization length was found to be $ν=1.622\pm 0.035$. The mulifractal function, $f(α)$, appears to be universal, however, the exponents $D_q$ and $α_q$ produced anomalous variations along the phase boundary, $p_c^Q(E)$.

cond-mat.dis-nn↗
arXiv2014

On the generalized dimensions of multifractal eigenstates

Recently, based on heuristic arguments, it was conjectured that an intimate relation exists between any multifractal dimensions, $D_q$ and $D_{q'}$, of the eigenstates of critical random matrix ensembles: $D_{q'} \approx qD_q[q'+(q-q')D_q]^{-1}$, $1\le q, q' \le 2$. Here, we verify this relation by extensive numerical calculations on critical random matrix ensembles and extend its applicability to $q<1/2$ but also to deterministic models producing multifractal eigenstates and to generic multifractal structures. We also demonstrate, for the scattering version of the power-law banded random matrix model at criticality, that the scaling exponents $σ_q$ of the inverse moments of Wigner delay times, $\bra τ_{\tbox W}^{-q} \ket \propto N^{-σ_q}$ where $N$ is the linear size of the system, are related to the level compressibility $χ$ as $σ_q\approx q(1-χ)[1+qχ]^{-1}$ for a limited range of $q$; thus providing a way to probe level correlations by means of scattering experiments.

cond-mat.dis-nn↗
arXiv2014

A novel method of generating tunable underlying network topologies for social simulation

We propose a method of generating different scale-free networks, which has several input parameters in order to adjust the structure, so that they can serve as a basis for computer simulation of real-world phenomena. The topological structure of these networks was studied to determine what kind of networks can be produced and how can we give the appropriate values of parameters to get a desired structure.

cs.SI↗
arXiv2012

Multifractal dimensions for critical random matrix ensembles

Based on heuristic arguments we conjecture that an intimate relation exists between the eigenfunction multifractal dimensions $D_q$ of the eigenstates of critical random matrix ensembles $D_{q'} \approx qD_q[q'+(q-q')D_q]^{-1}$, $1\le q \le 2$. We verify this relation by extensive numerical calculations. We also demonstrate that the level compressibility $χ$ describing level correlations can be related to $D_q$ in a unified way as $D_q=(1-χ)[1+(q-1)χ]^{-1}$, thus generalizing existing relations with relevance to the disorder driven Anderson--transition.

cond-mat.dis-nn↗
arXiv2011

Quantum chaos in one dimension?

In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit, N->infinity, the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.

nlin.CD↗
arXiv2010

Scattering and transport statistics at criticality

We study numerically scattering and transport statistical properties of the one-dimensional Anderson model at the metal-insulator transition described by the Power-law Banded Random Matrix (PBRM) model at criticality. Within a scattering approach to electronic transport, we concentrate on the case of a small number of single-channel attached leads. We observe a smooth transition from localized to delocalized behavior in the average scattering matrix elements, the conductance probability distribution, the variance of the conductance, and the shot noise power by varying $b$ (the effective bandwidth of the PBRM model) from small ($b\ll 1$) to large ($b>1$) values. We contrast our results with analytic random matrix theory predictions which are expected to be recovered in the limit $b\to \infty$. We also compare our results for the PBRM model with those for the three-dimensional (3D) Anderson model at criticality, finding that the PBRM model with $b \in [0.2,0.4]$ reproduces well the scattering and transport properties of the 3D Anderson model.

cond-mat.dis-nn↗
arXiv2007

Entanglement in Disordered Systems at Criticality

Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or quantum computation. In this work we investigate an extended system of N qubits. In our system a qubit is the absence or presence of an electron at a site of a tight-binding system. Several measures of entanglement between a given qubit and the rest of the system and also the entanglement between two qubits and the rest of the system is calculated in a one-electron picture in the presence of disorder. We invoke the power law band random matrix model which even in one dimension is able to produce multifractal states that fluctuate at all length scales. The concurrence, the tangle and the entanglement entropy all show interesting scaling properties.

cond-mat.dis-nn↗
arXiv2007

Electron-electron Relaxation in Disordered Interacting Systems

We study the relaxation of a non-equilibrium carrier distribution under the influence of the electron-electron interaction in the presence of disorder. Based on the Anderson model, our Hamiltonian is composed from a single particle part including the disorder and a two-particle part accounting for the Coulomb interaction. We apply the equation-of-motion approach for the density matrix, which provides a fully microscopic description of the relaxation. Our results show that the nonequlibrium distribution in this closed and internally interacting system relaxes exponentially fast during the initial dynamics. This fast relaxation can be described by a phenomenological damping rate. The total single particle energy decreases in the redistribution process, keeping the total energy of the system fixed. It turns out that the relaxation rate decreases with increasing disorder.

cond-mat.dis-nn↗
arXiv2003

Structure formation in binary colloids

A theoretical study of the structure formation observed very recently [Phys. Rev. Lett. 90, 128303 (2003)] in binary colloids is presented. In our model solely the dipole-dipole interaction of the particles is considered, electrohidrodynamic effects are excluded. Based on molecular dynamics simulations and analytic calculations we show that the total concentration of the particles, the relative concentration and the relative dipole moment of the components determine the structure of the colloid. At low concentrations the kinetic aggregation of particles results in fractal structures which show a crossover behavior when increasing the concentration. At high concentration various lattice structures are obtained in a good agreement with experiments.

cond-mat.soft↗
arXiv2003

Dynamics of short time--scale energy relaxation of optical excitations due to electron--electron scattering in the presence of arbitrary disorder

A non--equilibrium occupation distribution relaxes towards the Fermi--Dirac distribution due to electron--electron scattering even in finite Fermi systems. The dynamic evolution of this thermalization process assumed to result from an optical excitation is investigated numerically by solving a Boltzmann equation for the carrier populations using a one--dimensional disordered system. We focus on the short time--scale behavior. The logarithmically long time--scale associated with the glassy behavior of interacting electrons in disordered systems is not treated in our investigation. For weak disorder and short range interaction we recover the expected result that disorder enhances the relaxation rate as compared to the case without disorder. For sufficiently strong disorder, however, we find an opposite trend due to the reduction of scattering probabilities originating from the strong localization of the single--particle states. Long--range interaction in this regime produces a similar effect. The relaxation rate is found to scale with the interaction strength, however, the interplay between the implicit and the explicit character of the interaction produces an anomalous exponent.

cond-mat.dis-nn↗
arXiv2002

Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions

We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0 and U=infinity eigenstates bases respectively. This implies the existence of a duality point U_d where the eigenstates have the same spreading in both bases. U_d is surrounded by an interval of finite width which is characterized by a non Lorentzian spreading of the strength function in both bases. Scaling arguments predict the survival of this intermediate regime as the number of particles is increased.

cond-mat.dis-nn↗