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Floquet Majorana Edge Mode and Non-Abelian Anyons in a Driven Kitaev Model

We theoretically study laser driven nonequilibrium states in the Kitaev honeycomb model with a magnetoelectric cross coupling. We show that a topological spin liquid with a gapless chiral edge mode emerges when we apply an elliptically or circularly polarized laser. This is a strongly correlated quantum spin version of the Floquet topological insulator. In the topological phase, the edge mode is made from Majorana fermions and the bulk has gapped non-Abelian anyon excitations.

cond-mat.str-el↗

Random graph ensembles with many short loops

Networks observed in the real world often have many short loops. This violates the tree-like assumption that underpins the majority of random graph models and most of the methods used for their analysis. In this paper we sketch possible research routes to be explored in order to make progress on networks with many short loops, involving old and new random graph models and ideas for novel mathematical methods. We do not present conclusive solutions of problems, but aim to encourage and stimulate new activity and in what we believe to be an important but under-exposed area of research. We discuss in more detail the Strauss model, which can be seen as the `harmonic oscillator' of `loopy' random graphs, and a recent exactly solvable immunological model that involves random graphs with extensively many cliques and short loops.

cond-mat.dis-nn↗

The generating function for the connected correlator in the random energy model and its effective potential

Starting with two copies of the random energy model coupled with independent magnetic fields, the generating function for the connected correlator of the magnetization is exactly derived. Without use of the replica trick, it is shown that the Hessian of the generating function is symmetric under exchanging the two copies when the system is finite, but the symmetry is spontaneously broken in the low-temperature phase. It can be regarded as a rigorous realization of the replica symmetry breaking. The corresponding effective potential, which has two independent variables conjugate to the magnetic fields, is also calculated. It is singular when the two variables coincide. The singularity is consistent with that observed in the effective potentials of short-ranged disordered systems in the context of the functional renormalization group.

cond-mat.dis-nn↗

Interplay between boundaries and disorder in coupled optical waveguides

We investigate the effects of weak disorder on the time evolution of a wave packet in an array of optical waveguides with parity-symmetric evanescent coupling and, open or periodic boundary conditions. For an open array, when the disorder is unable to suppress the ballistic expansion, we find that the light partially localizes to its initial waveguide and the parity-symmetric waveguide when a single waveguide is excited. For an array with periodic boundary condition, the light localizes in the initial waveguide and its antipodal waveguide. Through a model where the boundaries of the array are only partially reflective, we quantify and investigate the continuous crossover between these two regimes. Our results show that disorder-induced localization in finite arrays with very weak disorder is strongly affected by the boundary effects that have been hitherto ignored.

physics.optics↗

On the spectrum of the discrete $1d$ Schrödinger operator with an arbitrary even potential

The discrete one-dimensional Schrödinger operator is studied in the finite interval of length $N=2 M$ with the Dirichlet boundary conditions and an arbitrary potential even with respect to the spacial reflections. It is shown, that the eigenvalues of such a discrete Schrödinger operator (Hamiltonian), which is represented by the $2M\times2M$ tridiagonal matrix, satisfy a set of polynomial constrains. The most interesting constrain, which is explicitly obtained, leads to the effective Coulomb interaction between the Hamiltonian eigenvalues. In the limit $M\to\infty$, this constrain induces the requirement, which should satisfy the scattering date in the scattering problem for the discrete Schrödinger operator in the half-line. We obtain such a requirement in the simplest case of the Schrödinger operator, which does not have bound and semi-bound states, and which potential has a compact support.

math-ph↗

One-dimensional excitonic systems with diagonal Lévy disorder: A detailed study of the absorption spectra and the disorder scaling of localization length

We present a detailed study of the effects of Lévy $α$-stable disorder distributions on the optical and localization properties of excitonic systems. These distributions are a generalization of commonly studied Gaussian randomness ($α= 2$). However, the more general case ($α< 2$) includes also heavy-tailed behavior with a divergent second moment. These types of distributions give rise to novel effects, such as exchange broadening of the absorption spectra and anomalous localization of the excitonic states, which has been found in various excitonic systems. We provide a thorough examination of the localization behavior and the absorption spectra of excitons in chains with Lévy $α$-stable diagonal disorder. Several regimes are considered in detail: (i) weak disorder and small systems, where finite size effects become significant; (ii) intermediate disorder and/or larger systems for which exciton states around the exciton band edge spread over a number of monomers, and (iii) strong disorder where the exciton wave functions resemble the individual molecular states. We propose analytical approaches to describe the disorder scaling of relevant quantities for these three regimes of localization, which match excellently with numerical results. We also show the appearance of short localization segments caused by outliers (monomers having transition energies larger than the exciton band width). Such states give rise to an additional structure in the absorption spectrum, density of states, and in the nontrivial disorder scaling of the absorption band width.

cond-mat.dis-nn↗

Entropies of tailored random graph ensembles: bipartite graphs, generalised degrees, and node neighbourhoods

We calculate explicit formulae for the Shannon entropies of several families of tailored random graph ensembles for which no such formulae were as yet available, in leading orders in the system size. These include bipartite graph ensembles with imposed (and possibly distinct) degree distributions for the two node sets, graph ensembles constrained by specified node neighbourhood distributions, and graph ensembles constrained by specified generalised degree distributions.

cond-mat.dis-nn↗

Hidden Quasicrystal in Hofstadter Butterfly

Topological description of hierarchical sets of spectral gaps of Hofstadter butterfly is found to be encoded in a quasicrystal where magnetic flux plays the role of a phase factor that shifts the origin of the quasiperiodic order. Revealing an intrinsic frustration at smallest energy scale, described by $ζ=2-\sqrt{3}$, this irrational number characterizes the universal butterfly and is related to two quantum numbers that includes the Chern number of quantum Hall states. With a periodic drive that induces phase transitions in the system, the fine structure of the butterfly is shown to be amplified making states with large topological invariants accessible experimentally .

cond-mat.dis-nn↗

Numerical simulations of stick percolation: Application to the study of structured magnetorheologial elastomers

In this article we explore how structural parameters of composites filled with one-dimensional, electrically conducting elements (such as sticks, needles, chains, or rods) affect the percolation properties of the system. To this end, we perform Monte Carlo simulations of asymmetric two-dimensional stick systems with anisotropic alignments. We compute the percolation probability functions in the direction of preferential orientation of the percolating objects and in the orthogonal direction, as functions of the experimental structural parameters. Among these, we considered the average length of the sticks, the standard deviation of the length distribution, and the standard deviation of the angular distribution. We developed a computer algorithm capable of reproducing and verifying known theoretical results for isotropic networks and which allows us to go beyond and study anisotropic systems of experimental interest. Our research shows that the total electrical anisotropy, considered as a direct consequence of the percolation anisotropy, depends mainly on the standard deviation of the angular distribution and on the average length of the sticks. A conclusion of practical interest is that we find that there is a wide and well-defined range of values for the mentioned parameters for which it is possible to obtain reliable anisotropic percolation under relatively accessible experimental conditions when considering composites formed by dispersions of sticks, oriented in elastomeric matrices.

cond-mat.soft↗

Resonant metallic states in driven quasiperiodic lattices

We consider a quasiperiodic Aubry-Andre (AA) model and add a weak time-periodic and spatially quasiperiodic perturbation. The undriven AA model is chosen to be well in the insulating regime. The spatial quasiperiodic perturbation extends the model into two dimensions in reciprocal space. For a spatial resonance which reduces the reciprocal space dynamics to an effective one-dimensional two-leg ladder case, the ac perturbation resonantly couples certain groups of localized eigenstates of the undriven AA model and turns them into extended metallic ones. Slight detuning of the spatial and temporal frequencies off resonance returns these states into localized ones. We analyze the details of the resonant metallic eigenstates using Floquet representations. In particular, we find that their size grows linearly with the system size. Initial wave packets overlap with resonant metallic eigenstates and lead to ballistic spreading.

cond-mat.dis-nn↗

Certain General Constraints on the Many-Body Localization Transition

Isolated quantum systems at strong disorder can display many-body localization (MBL), a remarkable phenomena characterized by an absence of conduction even at finite temperatures. As the ratio of interactions to disorder is increased, one expects that an MBL phase will eventually undergo a dynamical phase transition to a delocalized phase. Here we constrain the nature of such a transition by exploiting the strong subadditivity of entanglement entropy, as applied to the many-body eigenstates close to the transition in general dimensions. In particular, we show that at a putative continuous transition between an MBL and an ergodic delocalized phase, the critical eigenstates are necessarily thermal, and therefore, the critical entanglement entropy equals the thermal entropy. We also explore a qualitatively different continuous localization-delocalization transition, where the delocalized phase is non-ergodic whose volume law entanglement entropy tends to zero as the transition is approached.

cond-mat.dis-nn↗

Quantfying rich patterns in agglomeration of floating beads

Macroscopic spherical particles spontaneously form rich patterns on a standing Faraday wave. These patterns are found to follow a very systematic trend depending on the floater concentration $ϕ$: The same floaters that accumulate at amplitude maxima (antinodes) of the wave at low $ϕ$, surprisingly move towards the nodal lines when $ϕ$ is beyond a certain value. In more detail, circular irregularly packed antinode clusters at low $ϕ$ give way to loosely packed filamentary structures at intermediate $ϕ$, and are then followed by densely packed grid-shaped node clusters at high $ϕ$. Here, we successfully characterize the morphology of these rich patterns using a metric analysis, i.e., the Minkowski functionals. We modify the Minkowski functionals such that we are able to measure the physical quantities of the clusters such as area, perimeter, and aspect ratio.

physics.flu-dyn↗

Aspects of Statistical Physics in Computational Complexity

The aim of this review paper is to give a panoramic of the impact of spin glass theory and statistical physics in the study of the K-sat problem. The introduction of spin glass theory in the study of the random K-sat problem has indeed left a mark on the field, leading to some groundbreaking descriptions of the geometry of its solution space, and helping to shed light on why it seems to be so hard to solve. Most of the geometrical intuitions have their roots in the Sherrington-Kirkpatrick model of spin glass. We'll start Chapter 2 by introducing the model from a mathematical perspective, presenting a selection of rigorous results and giving a first intuition about the cavity method. We'll then switch to a physical perspective, to explore concepts like pure states, hierarchical clustering and replica symmetry breaking. Chapter 3 will be devoted to the spin glass formulation of K-sat, while the most important phase transitions of K-sat (clustering, condensation, freezing and SAT/UNSAT) will be extensively discussed in Chapter 4, with respect their complexity, free-entropy density and the Parisi 1RSB parameter. The concept of algorithmic barrier will be presented in Chapter 5 and exemplified in detail on the Belief Propagation (BP) algorithm. The BP algorithm will be introduced and motivated, and numerical analysis of a BP-guided decimation algorithm will be used to show the role of the clustering, condensation and freezing phase transitions in creating an algorithmic barrier for BP. Taking from the failure of BP in the clustered and condensed phases, Chapter 6 will finally introduce the Cavity Method to deal with the shattering of the solution space, and present its application to the development of the Survey Propagation algorithm.

cs.CC↗

Local structure of supercritical matter

The supercritical state is currently viewed as uniform on the pressure-temperature phase diagram. Supercritical fluids have the dynamic motions of a gas but are able to dissolve materials like a liquid. They have started to be deployed in many important industrial applications stimulating fundamental theoretical work and development of experimental techniques. Here, we have studied local structure of supercritical matter by calculating static structure factor, mean force potential, self-diffusion, first coordination shell number and pair distribution function within very wide temperature ranges. Our results show a monotonic disappearance of medium-range order correlations at elevated temperatures providing direct evidence for structural crossover in the reciprocal and real spaces. Importantly, the discovered structural crossover in the reciprocal space is fundamentally inter-related to structural crossover in the real space, granting new unexpected interlinks between operating system properties in the supercritical state. Finally, we discuss an evolution analysis of the local structure and important implications for an experimental detection of structural monotonic transitions in the supercritical matter.

cond-mat.stat-mech↗

Topology of delocalization in the nonlinear Anderson model and anomalous diffusion on finite clusters

This study is concerned with destruction of Anderson localization by a nonlinearity of the power-law type. We suggest using a nonlinear Schrödinger model with random potential on a lattice that quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. For super-quadratic nonlinearity the borderline spreading corresponds to diffusion processes on finite clusters. We have proposed an analytical method to predict and explain such transport processes. Our method uses a topological approximation of the nonlinear Anderson model and, if the exponent of the power nonlinearity is either integer or half-integer, will yield the wanted value of the transport exponent via a triangulation procedure in an Euclidean mapping space. A kinetic picture of the transport arising from these investigations uses a fractional extension of the diffusion equation to fractional derivatives over the time, signifying non-Markovian dynamics with algebraically decaying time correlations.

cond-mat.stat-mech↗

Fractional Einstein relation for strongly disordered semiconductors

A novel Einstein relation (fractional Einstein relation, FER) for the electric conduction in non-crystalline semiconductors is presented. FER and the generalized Einstein relation (GER) [Phys. Rev. E 8, 1296 (1998)] are compared to the result of the Monte Carlo (MC) simulation, and is confirmed that FER exhibits better agreement than GER. The cruial feature of FER is that it reflects the violation of the detailed balance in the coarse-grained hopping process, while it is preserved in the original Einstein relation or GER.

cond-mat.dis-nn↗

Reentrance in an active spin glass model

Active matter, whose motion is driven, and glasses, whose dynamics are arrested, seem to lie at opposite ends of the spectrum in nonequilibrium systems. In spite of this, both classes of systems exhibit a multitude of stable states that are dynamically isolated from one another. While this defining characteristic is held in common, its origin is different in each case: for active systems, the irreversible driving forces can produce dynamically frozen states, while glassy systems vitrify when they get kinetically trapped on a rugged free energy landscape. In a mixture of active and glassy particles, the interplay between these two tendencies leads to novel phenomenology. We demonstrate this with a spin glass model that we generalize to include an active component. In the absence of a ferromagnetic bias, we find that the spin glass transition temperature depresses with the active fraction, consistent with what has been observed for fully active glassy systems. When a bias does exist, however, a new type of transition becomes possible: the system can be cooled out of the glassy phase. This unusual phenomenon, known as reentrance, has been observed before in a limited number of colloidal and micellar systems, but it has not yet been observed in active glass mixtures. Using low order perturbation theory, we study the origin of this reentrance and, based on the physical picture that results, suggest how our predictions might be measured experimentally.

cond-mat.stat-mech↗

Criteria of amorphous solidification

A different perspective on the long-standing problem of amorphous solidification is offered, based on an alternative definition of a solid as a porous medium. General, model-free results are obtained concerning the growing dynamic length accompanying solidification and its relation to the growing relaxation time. Criteria are derived for the dynamic length to diverge and for its divergence to entail the arrest of particle motion.

cond-mat.dis-nn↗