Atto-localization in a one-dimensional lattice

We investigate the dielectric resonance, local field distribution and effective optical response in the fractal structured metallic-dielectric composites using the Green's function formalism. With the evolution of the fractal level, similarity of the density of states (DOS) of dielectric resonances appears due to the self-similar structure, as well as of the inverse participation ratio (IPR) (which is used to represent the localization of field) of local field, and the effective linear optical responses. For a self-similar defect, when the difference admittance ratio $\ensuremath{\eta}\phantom{\rule{0.2em}{0ex}}[=({ϵ}_{2}\ensuremath{-}{ϵ}_{0})∕({ϵ}_{1}\ensuremath{-}{ϵ}_{0})]⪡0$ or $\ensuremath{\eta}⪢1$, DOS and IPR of the defect modes also exhibit the similarity or antisimilarity. However, for $\ensuremath{\eta}∊(\ensuremath{-}1,2)$, the spectra of DOS and IPR become more complicated as the defect modes overlap the original modes. Finally, the existence of the self-similar defect has no obvious influence on the effective optical responses.

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with non-Hermitian either uniform or staggered quasiperiodic potentials. We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones, which implies that the system has mobility edges. The localization transition is accompanied by the symmetry breaking transition. While if the non-Hermitian quasiperiodic disorder is staggered, we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis. Interestingly, some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters. The reentrant localization transitions are associated with the intermediate phases hosting mobility edges. Besides, we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives. More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum, inverse participation ratio, and normalized participation ratio.

We analyze the out-of-equilibrium dynamics of a quantum particle coupled to local magnetic degrees of freedom that undergo a classical phase transition. Specifically, we consider a two-dimensional tight-binding model that interacts with a background of classical spins in thermal equilibrium, which are subject to Ising interactions and act as emergent, correlated disorder for the quantum particle. Particular attention is devoted to temperatures close to the ferromagnet-to-paramagnet transition. To capture the salient features of the classical transition, namely the effects of long-range correlations, we focus on the strong coupling limit, in which the model can be mapped onto a quantum percolation problem on spin clusters generated by the Ising model. By inspecting several dynamical probes such as energy level statistics, inverse participation ratios, and wave-packet dynamics, we provide evidence that the classical phase transition might induce a delocalization-localization transition in the quantum system at certain energies. We also identify further important features due to the presence of Ising correlations, such as the suppression of compact localized eigenstates.

We study the quantum statistical electronic properties of random networks which inherently lack a fixed spatial dimension. We use tools like the density of states (DOS) and the inverse participation ratio to uncover various phenomena, such as unconventional properties of the energy spectrum and persistent localized states (PLS) at various energies, corresponding to quantum phases with zero-dimensional (0D) and one-dimensional (1D) order. For small ratio of edges over vertices in the network R we find properties resembling graphene(honeycomb) lattices, like a similar DOS containing a linear dispersion relation at the band center at energy E=0. In addition, we find PLS at various energies including E=-1,0,1, and others, for example, related to the golden ratio. At E=0 the PLS lie at vertices that are not directly connected with an edge, due to partial bipartite symmetries of the random networks (0D order). At E=-1,1 the PLS lie mostly at pairs of vertices (bonds), while the rest of the PLS at other energies, like the ones related to the golden ratio, lie at lines of vertices of fixed length (1D order), at the spatial boundary of the network, resembling the edge states in confined graphene systems with zigzag edges. As the ratio R is increased the DOS of the network approaches the Wigner semicircle, corresponding to random symmetric matrices(Hamiltonians) and the PLS are reduced and gradually disappear as the connectivity in the network increases. Finally, we calculate the spatial dimension D of the network and its fluctuations. We obtain both integer and noninteger D and a logarithmic dependence on R. In addition, we examine the relation of D and its fluctuations to the electronic properties derived. Our results imply that universal physics can manifest in physical systems irrespectively of their spatial dimension. Relations to emergent spacetime in quantum and emergent gravity approaches are also discussed.

Presents the first calculations of the electronic density of states, the electrical conductivity and the inverse participation ratio as a function of energy for a large model of hydrogenated amorphous silicon. The model contains 1555 Si atoms and 400 H atoms and all Si atoms are fourfold coordinated. This model has a clear gap in the density of electronic states. The 'mobility gap' (estimated from the conductivity versus energy curves) is about 0.6 eV wider than the gap in the electronic density of states. The authors also present for comparison the same calculations on a defected model of amorphous Si with 1728 atoms which contains states within the gap arising mainly from departure from tetrahedral geometry.

The generalization of the Dyson Brownian motion approach of random matrices to Anderson localization (AL) models (Chalker et al 1996 Phys. Rev. Lett. 77 554) and to many-body localization (MBL) Hamiltonians (Serbyn and Moore 2015 arXiv:1508.07293) is revisited to extract the level repulsion exponent β, where in the delocalized phase governed by the Wigner–Dyson statistics, , in the localized phase governed by the Poisson statistics, and at the critical point. The idea is that the Gaussian disorder variables hi are promoted to Gaussian stationary processes hi(t) in order to sample the disorder stationary distribution with some time correlation τ. The statistics of energy levels can then be studied via Langevin and Fokker–Planck equations. For the MBL quantum spin Hamiltonian with random fields hi, we obtain in terms of the Edwards–Anderson matrix for the same eigenstate m = n and for consecutive eigenstates m = n + 1. For the Anderson localization tight-binding Hamiltonian with random on-site energies hi, we find in terms of the density correlation matrix for consecutive eigenstates m = n + 1, while the diagonal element m = n corresponds to the inverse participation ratio of the eigenstate .

Discrete- and continuous-time approaches are frequently used to model the role of heterogeneity on dynamical interacting agents on the top of complex networks. While, on the one hand, one does not expect drastic differences between these approaches, and the choice is usually based on one's expertise or methodological convenience, on the other hand, a detailed analysis of the differences is necessary to guide the proper choice of one or another approach. We tackle this problem by investigating both discrete- and continuous-time mean-field theories for the susceptible-infected-susceptible (SIS) epidemic model on random networks with power-law degree distributions. We compare the discrete epidemic link equations(ELE) and continuous pair quenched mean-field (PQMF) theories with the corresponding stochastic simulations, both theories that reckon pairwise interactions explicitly. We show that ELE converges to the PQMF theory when the time step goes to zero. We performed an epidemic localization analysis considering the inverse participation ratio (IPR). Both theories present the same localization dependence on network degree exponent γ: for γ<5/2 the epidemics are localized on the maximum k-core of networks with a vanishing IPR in the infinite-size limit while, for γ>5/2, the localization happens on hubs that do not form a densely connected set and leads to a finite value of the IPR. However, the IPR and epidemic threshold of ELE depend on the time-step discretization such that a larger time step leads to more localized epidemics. A remarkable difference between discrete- and continuous-time approaches is revealed in the epidemic prevalence near the epidemic threshold, in which the discrete-time stochastic simulations indicate a mean-field critical exponent θ=1 instead of the value θ=1/(3-γ) obtained rigorously and verified numerically for the continuous-time SIS on the same networks.

A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules–atoms in coexistence in the other one. The usual markers for this phase transition are the ground state energy and the expected value of the number of atoms (alternatively, the number of molecules) in the ground state. In this work, other markers for the QPT, such as the inverse participation ratio (IPR), and particularly, the Rényi entropy, are analyzed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT.

Universal spectral properties of multiplex networks allow us to assess the nature of the transition between disease-free and endemic phases in the SIS epidemic spreading model. In a multiplex network, depending on a coupling parameter, p, the inverse participation ratio (IPR) of the leading eigenvector of the adjacency matrix can be in two different structural regimes: (i) layer-localized and (ii) delocalized. Here we formalize the structural transition point, p*, between these two regimes, showing that there are universal properties regarding both the layer size n and the layer configurations. Namely, we show that IPR ∼ n −δ , with δ ≈ 1, and revealed an approximately linear relationship between p* and the difference between the layers’ average degrees. Furthermore, we showed that this multiplex structural transition is intrinsically connected with the nature of the SIS phase transition, allowing us to both understand and quantify the phenomenon. As these results are related to the universal properties of the leading eigenvector, we expect that our findings might be relevant to other dynamical processes in complex networks.

We investigate the effects of two types of disorder on the electronic density of states of III-V semiconductors using simple tight-binding models and the empirical pseudopotential method. For the first type of disorder we consider a stoichiometric system with fourfold coordination, all bonds satisfied, variations in the bond lengths and angles, and only unlike-atom bonds. The second type of disorder includes the properties of the first with the addition of like-atom bonds. These two types of disorder are studied explicitly by taking GaAs as a prototype and making various GaAs structures using the atomic positions of certain crystal structures with short-range disorder. These structures are crystals; however, they have atoms in the primitive cells arranged in varying fashions. A comparison of the trends observed in the densities of states with the inclusion of different types of disorder reveals valuable information concerning the relationship of the structural nature of an amorphous system to its density of states. We present a model of the density of states of our amorphous prototype GaAs, for each type of disorder, which we believe would be consistent with some of the present experimental radial-distribution-function data. The effects of these types of disorder are discussed in general, and hopefully they will be useful in identifying specific types of disorder in amorphous samples.

Electron-hole subbands at the GaSbInAs interface

The driven dynamics of localization transitions in a non-Hermitian Disordered Aubry-André (DAA) model are examined under both open boundary conditions (OBC) and periodic boundary conditions (PBC). Through an analysis of the static properties of observables, including the localization length ($ξ$), inverse participation ratio ($\rm IPR$), and energy gap ($ΔE$), we found that the critical exponents examined under PBC are also applicable under OBC. The Kibble-Zurek scaling (KZS) for the driven dynamics in the non-Hermitian DAA systems is formulated and numerically verified for different local-to-local quench directions. The hybrid KZS (HKZS) in the overlapping critical region of non-Hermitian DAA and Anderson localization is proposed and numerically confirmed the validity across a local-to-skin quench direction. This study generalizes the application of the KZS to the dynamical localization transitions within systems featuring dual localization mechanisms.

Non-Hermitian quasicrystals possess and metal–insulator transitions induced by gain and loss or nonreciprocal effects. In this work, we uncover the nature of localization transitions in a generalized Aubry–André–Harper model with dimerized hopping amplitudes and complex onsite potential. By investigating the spectrum, adjacent gap ratios and inverse participation ratios, we find an extended phase, a localized phase and a mobility edge phase, which are originated from the interplay between hopping dimerizations and non-Hermitian onsite potential. The lower and upper bounds of the mobility edge are further characterized by a pair of topological winding numbers, which undergo quantized jumps at the boundaries between different phases. Our discoveries thus unveil the richness of topological and transport phenomena in dimerized non-Hermitian quasicrystals.

The relationship of topology and disorder in a 1D Su–Schrieffer–Heeger chain subjected to a slowly varying quasi‐periodic modulation is uncovered. By numerically calculating the disorder‐averaged winding number and analytically studying the localization length of the zero modes, the topological phase diagram is obtained, which implies that the topological Anderson insulator (TAI) can be induced by a slowly varying quasi‐periodic modulation. Moreover, unlike the localization properties in the TAI phase caused by random disorder, mobility edges can enter into the TAI region identified by the fractal dimension, the inverse participation ratio, and the spatial distributions of the wave functions, the boundaries of which coincide with the analytical results presented here.

We propose coherent (‘Schrödinger cat-like’) states adapted to the parity symmetry providing a remarkable variational description of the ground and first excited states of vibron models for finite (N)-size molecules. Vibron models undergo a quantum shape phase transition (from linear to bent) at a critical value ξc of a control parameter. These trial cat states reveal a sudden increase in vibration–rotation entanglement linear (L) and von Neumann (S) entropies from zero to (to be compared with L(N)max(ξ) = 1 − 1/(N + 1)) and , respectively, above the critical point, ξ > ξc, in agreement with exact numerical calculations. We also compute inverse participation ratios, for which these cat states capture a sudden delocalization of the ground-state wave packet across the critical point. Analytic expressions for entanglement entropies and inverse participation ratios of variational states, as functions of N and ξ, are given in terms of hypergeometric functions.