Random Dimer Research Articles

Toward Gaussian Process Regression Modeling of a Urea Force Field.

FFLUX is a next-generation, machine-learnt force field built on three cornerstones: quantum chemical topology, Gaussian process regression, and (high-rank) multipolar electrostatics. It is capable of performing molecular dynamics with near-quantum accuracy at a lower computational cost than standard ab initio molecular dynamics. Previous work with FFLUX was concerned with water and formamide. In this study, we go one step further and challenge FFLUX to model urea, a larger and more flexible system. In result, we have trained urea models at the B3LYP/aug-cc-pVTZ level of theory, with a mean absolute error of 0.4 kJ mol-1 and a maximum prediction error below 7.0 kJ mol-1. To test their performance in molecular dynamics simulations, two sets of FFLUX geometry optimizations were carried out: 5 dimers corresponding to energy minima and 75 random dimers. The 5 dimers were recovered with a root-mean-square deviation below 0.1 Å with respect to their ab initio references. Out of the 75 random dimers, 68% converged to the qualitatively same dimer as those obtained at the ab initio level. Furthermore, we have ranked the 5 FFLUX-optimized dimers in the order of their relative FFLUX single-point energies and compared them with the ab initio method. The energy ranking fully agreed but for one crossover between two successive minima. Finally, we have demonstrated the importance of geometry-dependent (i.e., flexible) multipole moments, showing that the lack of multipole moment flexibility can lead to average errors in the total intermolecular electrostatic energy of more than 2 orders of magnitude.

Extended states in random dimer gated graphene superlattices

Ordered and disordered semiconductor superlattices represent structures with completely opposed properties. For instance, ordered superlattices exhibit extended Bloch-like states, while disordered superlattices present localized states. These characteristics lead to higher conductance in ordered superlattices compared to disordered ones. Surprisingly, disordered dimer superlattices, which consist of two types of quantum wells with one type always appearing in pairs, exhibit extended states. The percentage of dissimilar wells does not need to be large to have extended states. Furthermore, the conductance is intermediate between ordered and disordered superlattices. In this work, we explore disordered dimer superlattices in graphene. We calculate the transmission and transport properties using the transfer matrix method and the Landauer–Büttiker formalism, respectively. We identify and discuss the main energy regions where the conductance of random dimer superlattices in graphene is intermediate to that of ordered and disordered superlattices. We also analyze the resonant energies of the double quantum well cavity and the electronic structure of the host gated graphene superlattice (GGSL), finding that the coupling between the resonant energies and the superlattice energy minibands gives rise to the extended states in random dimer GGSLs.

Edge-pinning effect of graphene nanoflakes sliding atop graphene

Edge effect is one of the detrimental factors preventing superlubricity in laminar solid lubricants. Separating the friction contribution from the edge atom and inner atom is of paramount importance for rational design of ultralow friction across scales in van der Waals heterostructures. To decouple these contributions and provide the underlying microscopic origin at the atomistic level, we considered two contrast models, namely, graphene nanoflakes with dimerized and pristine edges sliding on graphene monolayer based on extensive ab initio calculations. On one hand, we found edge pinning effect by dimerization is obvious for misaligned contact. This case providing local commensuration along edges is reminiscent of Aubry’s pinned phase. The contribution of per dimerized edge carbon atom to the sliding potential energy corrugation is even 1.5 times more than that of an atom in bilayer graphene under commensurate contact. Thus, the dynamic and random edge dimerization during sliding will impact the tribological properties significantly and may be the important sources to account for the marked discrepancies in measured friction parameters [Qu et al., Phys. Rev. Lett. 2020, 125, 126102]. On the other hand, we found the edge contribution to friction is lattice orientation dependent and suppressed in aligned contact. This rationalizes the experimental finding where friction is dominated by interior atoms rather than edge pinning [Liao et al., Nat. Mater. 2022, 21, 47–53]. To eliminate the undesirable edge effects, we adopt strain engineering and edge fluorination to the tribological system constructed here. However, dimerized edges as high frictional pinning sites are robust to both approaches. We hope the detailed atomic information identified here would help for improving superlubric systems.

Asymptotics of pure dimer coverings on rail yard graphs

Abstract We study the asymptotic limit of random pure dimer coverings on rail yard graphs when the mesh sizes of the graphs go to 0. Each pure dimer covering corresponds to a sequence of interlacing partitions starting with an empty partition and ending in an empty partition. Under the assumption that the probability of each dimer covering is proportional to the product of weights of present edges, we obtain the limit shape (law of large numbers) of the rescaled height functions and the convergence of the unrescaled height fluctuations to a diffeomorphic image of the Gaussian free field (Central Limit Theorem), answering a question in [7]. Applications include the limit shape and height fluctuations for pure steep tilings [9] and pyramid partitions [20; 36; 39; 38]. The technique to obtain these results is to analyze a class of Macdonald processes which involve dual partitions as well.

Localization by particle–hole symmetry breaking: a loop expansion

Localization by a broken particle–hole (PH) symmetry in a random system of non-interacting quantum particles is studied on a d-dimensional lattice. Our approach is based on a chiral symmetry argument and the corresponding invariant measure, where the latter is described by a Grassmann functional integral. Within a loop expansion we find for small loops diffusion in the case of PH symmetry. Breaking the PH symmetry results in the creation of random dimers, which suppress diffusion and lead to localization on the scale , where D is the effective diffusion coefficient at PH symmetry and μ is the parameter related to PH symmetry breaking.

Experimental evidence for a valence-bond glass in the 5d1 double perovskite Ba2YWO6

We report the magnetic susceptibility, specific heat, and muon spin relaxation results of the $5{d}^{1}$ double perovskite ${\mathrm{Ba}}_{2}{\mathrm{YWO}}_{6}$. The dc magnetic susceptibility shows two distinct Curie-Weiss regimes and a sub-Curie-Weiss increase ${T}^{\ensuremath{-}n}$ with $n=0.75(1)$ for $T=3\text{--}100$ K, alluding to the presence of random magnetism. The ac magnetic susceptibility reveals a spin freezing at ${T}_{f}\ensuremath{\sim}0.3$ K with the activation energy of $\mathrm{\ensuremath{\Delta}}/{k}_{B}=27.6$ K. The specific heat data exhibit the pseudogap behavior at 25 K and the subsequent power-law dependence with decreasing temperature, indicating the gradual spin freezing with the quenching of orbital fluctuations. However, the muon spin relaxation data display only a weak muon spin depolarization with lacking long-range magnetic ordering down to 26 mK. Taken together, our results suggest that ${\mathrm{Ba}}_{2}{\mathrm{YWO}}_{6}$ is the proximate realization of a random spin-orbit dimer state.

A two-dimensional disordered magnetic metamaterial

We study the effect of a resonant frequency disorder on the eigenstates and the transport of magnetic energy in a two-dimensional (square) array of split-ring resonators (SRRs). In the absence of disorder, we find the dispersion relation of magneto-inductive waves and the mean square displacement (MSD) in closed form, showing that at long times the MSD is ballistic. When disorder is present, we consider two types: the usual Anderson distribution (uncorrelated monomers) and 2×2 units assigned at random to lattice sites (correlated tetramers). This is a direct extension to two dimensions of the one-dimensional random dimer model (RDM). For the uncorrelated case, we see saturation of the MSD for all disorder widths, while for the correlated case we find a disorder window, inside which the MSD does not saturate at long times, with an asymptotic sub-diffusive behavior MSD∼t0.26. Outside this disorder window, the MSD shows the same kind of saturation as in the monomer case. We conjecture that the sub-diffusive behavior is a remanent of a weak resonant transmission of a 2D plane wave across a tetramer unit.

Criticality and conformality in the random dimer model.

In critical systems, the effect of a localized perturbation affects points that are arbitrarily far from the perturbation location. In this paper, we study the effect of localized perturbations on the solution of the random dimer problem in two dimensions. By means of an accurate numerical analysis, we show that a local perturbation of the optimal covering induces an excitation whose size is extensive with finite probability. We compute the fractal dimension of the excitations and scaling exponents. In particular, excitations in random dimer problems on nonbipartite lattices have the same statistical properties of domain walls in spin glass. Excitations produced in bipartite lattices, instead, are compatible with a loop-erased self-avoiding random walk process. In both cases, we find evidence of conformal invariance of the excitations that is compatible with SLE_{κ} with parameter κ depending on the bipartiteness of the underlying lattice only.

Magnetic metamaterials with correlated disorder

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 (SRR), 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 shows an asymptotic behavior 〈n2〉∼tα, where α∼0 for uncorrelated disorder, and α>0 for the correlated case, spanning a whole range of behavior ranging from localization to super-diffusive behavior at finite system sizes. The transmission coefficient of a plane wave across a single magnetic dimer reveals the existence of well-defined regions in disorder strength-magnetic coupling space, where unit transmission for some wavevector(s) is possible. This explains the finite degree of mobility for magnetic excitations in the presence of correlated disorder, in the spirit of the random dimer model (Dunlap et al., 1990 [14]). Finally, the transmission of plane waves across an array with correlated disorder shows a power-law decrease with system size, in contrast to the exponential decrease found in the standard Anderson model.

Dominos in hedgehog domains

We introduce a new class of discrete approximations of planar domains that we call “hedgehog domains”. In particular, this class of approximations contains two-step Aztec diamonds and similar shapes. We show that fluctuations of the height function of a random dimer tiling on hedgehog discretizations of a planar domain converge in the scaling limit to the Gaussian Free Field with Dirichlet boundary conditions. Interestingly enough, in this case the dimer model coupling function satisfies the same Riemann-type boundary conditions as fermionic observables in the Ising model. In addition, using the same factorization of the double-dimer model coupling function as in [18], we show that in the case of approximations by hedgehog domains the expectation of the double-dimer height function is harmonic in the scaling limit.

Floquet dynamics of disordered bands with isolated critical energies

We investigate localization properties of driven models which exhibit a subextensive number of extended states in the static setting. We consider instances where the extended modes are or are not protected by topological considerations. To this end, we contrast the strongly driven, disordered, lowest Landau level, which we refer to as the random Landau model (RLM), with the random dimer model (RDM); the RDM also has a subextensive set of delocalized modes in the middle of the spectrum whose origin is not topological. We map the driven models on to a higher-dimensional effective model and numerically compute the localization length as a function of disorder strength, drive amplitude, and frequency using the recursive Green's function method. Our numerical results indicate that, in the presence of a strong drive (low frequency and/or large drive amplitude), the topologically protected RLM continues to exhibit a spectrum with both localized and delocalized (or critical) modes, but the spectral range of delocalized modes is enhanced by the driving. This occurs due to an admixture of the localized modes with extended modes arising due to the topologically protected critical energy in the middle of the spectrum. On the other hand, in the RDM, a weak drive immediately localizes the entire spectrum. This occurs in contrast to the naive expectation from perturbation theory that mixing between localized and delocalized modes generically enhances the delocalization of all modes. Our work highlights the importance of the origin of the delocalized modes in the localization properties of the corresponding Floquet model.

Density wave propagation in a two-dimensional random dimer potential: From a single to a bipartite square lattice

We study the propagation of a density perturbation in a weakly interacting boson gas confined on a lattice and in the presence of square dimerized impurities. Such a two-dimensional random-dimer model (2D-DRDM), previously introduced in [Capuzzi et al., Phys. Rev. A 92, 053622 (2015)], is the disorder transition from a single square lattice, where impurities are absent, to a bipartite square lattice, where the number of impurities is maximum and coincides with half the number of lattice sites. We show that disorder correlations can play a crucial role in the dynamics for a broad range of parameters by allowing density fluctuations to propagate in the 2D-DRDM lattice, even in the limit of strong disorder. In such a regime, the propagation speed depends on the percentage of impurities, interpolating between the speed in a single monoperiodic lattice and that in a bipartite one.

How Much Delocalisation is Needed for an Enhanced Area Law of the Entanglement Entropy?

We consider the random dimer model in one space dimension with Bernoulli disorder. For sufficiently small disorder, we show that the entanglement entropy exhibits at least a logarithmically enhanced area law if the Fermi energy coincides with a critical energy of the model where the localisation length diverges.

Violation of the Bell inequality in quantum critical random spin-1/2 chains

We investigate the entanglement and nonlocality properties of two random XX spin-1/2 critical chains, in order to better understand the role of breaking translational invariance to achieve nonlocal states in critical systems. We show that breaking translational invariance is a necessary but not sufficient condition for nonlocality, as the random chains remain in a local ground state up to a small degree of randomness. Furthermore, we demonstrate that the random dimer model does not have the same nonlocality properties of the translationally invariant chain, even though they share the same universality class for a certain range of randomness.

Charge transport properties in a one-dimensional description of polymer polyaniline

The metal-insulator transition taking place in Polyaniline (PAN) is investigated in a one-dimensional configuration when impurities are introduced by doping. The electronic transport is numerically analyzed, representing the system by a Hückel tight-binding Hamiltonian and using the non-equilibrium Green’s function formalism to obtain the conductance of the system under the presence of polaron and bipolaron doping. In a detailed analysis, we highlight the importance of studying extensive N sites chains, evaluating the conductance as a function of the de-coherence parameter η, decreasing it to the limit of 0+ ; this procedure allows us to study the existence of delocalized states in this system. It was possible to verify that although the bipolaron/polaron doping produces a displacement of the Fermi energy into a region of states outside the gap of the pure polymer, the conductance in the limit of zero inelastic scattering is zero, showing the existence of localized states at the Fermi level, due to disorder. This result indicates that the description of PAN as a linear one-dimensional object analyzed in a extensive N sites disordered chain does not manifest correlated disorder as proposed by the Random Dimer Model (RDM), where transport could occur because of the electronic states are extended. The lack of charge diffusion at the Fermi level in this one-dimensional description of the system shows that it is not an adequate model to study the metal-insulator transition when the polymer is doped. The incorporation of the nature of the polymerization process, introducing higher dimensional effects in its early stages, is possibly an essential ingredient to derive an appropriate model to describe the conducting behavior of the PAN system.

On anomalous Lieb–Robinson bounds for the Fibonacci XY chain

We rigorously prove a new kind of anomalous (or sub-ballistic) Lieb–Robinson bound for the isotropic XY chain with Fibonacci external magnetic field at arbitrary coupling. It is anomalous in that the usual exponential decay in |x|-v|t| is replaced by exponential decay in |x|-v|t|^\alpha with 0<\alpha<1 . In fact, we can characterize the values of \alpha for which such a bound holds as those exceeding \alpha_u^+ , the upper transport exponent of the one-body Fibonacci Hamiltonian. Following the approach of [14], we relate Lieb–Robinson bounds to dynamical bounds for the one-body Hamiltonian corresponding to the XY chain via the Jordan–Wigner transformation; in our case the one-body Hamiltonian with Fibonacci potential. We can bound its dynamics by adapting techniques developed in [8, 9, 2, 3] to our purposes. To our knowledge, this is the first rigorous derivation of anomalous quantum many-body transport. Along the way, we prove a new result about the one-body Fibonacci Hamiltonian: the upper transport exponent agrees with the time-averaged upper transport exponent, see Corollary 2.9. We also explain why our method does not extend to yield anomalous Lieb–Robinson bounds of power-law type for the random dimer model.

Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi–one-dimensionality

It is shown that an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight-binding model can be tailored to generate absolutely continuous energy bands. It can be achieved if linear atomic clusters of an appropriate size are side-coupled to a suitable subset of sites in the backbone, and if the nearest-neighbor hopping integrals, in the backbone and in the side-coupled cluster, bear a certain ratio. We work out the precise relationship between the number of atoms in one of the building blocks in the backbone and that in the side attachment. In addition, we also evaluate the definite correlation between the numerical values of the hopping integrals at different subsections of the chain, that can convert an otherwise point spectrum (or a singular continuous one for deterministically disordered lattices) with exponentially (or power law) localized eigenfunctions to an absolutely continuous spectrum comprising one or more bands (subbands) populated by extended, totally transparent eigenstates. The results, which are analytically exact, put forward a non-trivial variation of the Anderson localization (Anderson P. W., Phys. Rev., 109 (1958) 1492), pointing towards its unusual sensitivity to the numerical values of the system parameters and, go well beyond the other related models such as the Random Dimer Model (RDM) (Dunlap D. H. et al., Phys. Rev. Lett., 65 (1990) 88).

Transport of localized and extended excitations in chains embedded with randomly distributed linear and nonlinear n-mers.

We examine the transport of extended and localized excitations in one-dimensional linear chains populated by linear and nonlinear symmetric identical n-mers (with n=3, 4, 5, and 6), randomly distributed. First, we examine the transmission of plane waves across a single linear n-mer, paying attention to its resonances, and looking for parameters that allow resonances to merge. Within this parameter regime we examine the transmission of plane waves through a disordered and nonlinear segment composed by n-mers randomly placed inside a linear chain. It is observed that nonlinearity tends to inhibit the transmission, which decays as a power law at long segment lengths. This behavior still holds when the n-mer parameters do not obey the resonance condition. On the other hand, the mean square displacement exponent of an initially localized excitation does not depend on nonlinearity at long propagation distances z, and shows a superdiffusive behavior ∼z(1.8) for all n-mers, when parameters obey the resonance merging condition; otherwise the exponent reverts back to the random dimer model value ∼z(1.5).

Superdiffusive transport and energy localization in disordered granular crystals.

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to differ fundamentally from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder-an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements)-and for two types of initial conditions (displacement excitations and velocity excitations). We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics depend strongly on the type of initial condition. In particular, for displacement excitations, the long-time asymptotic behavior of the second moment m̃(2) of the energy has oscillations that depend on the type of disorder, with a complex trend that differs markedly from a power law and which is particularly evident for an Anderson-like disorder. By contrast, for velocity excitations, we find that a standard scaling m̃(2)∼t(γ) (for some constant γ) applies for all three types of disorder. For weakly precompressed (i.e., strongly nonlinear) chains, m̃(2) and the inverse participation ratio P(-1) satisfy scaling relations m̃(2)∼t(γ) and P(-1)∼t(-η), and the dynamics is superdiffusive for all of the cases that we consider. Additionally, when precompression is strong, the inverse participation ratio decreases slowly (with η<0.1) for all three types of disorder, and the dynamics leads to a partial localization around the core and the leading edge of a propagating wave packet. For an Anderson-like disorder, displacement perturbations lead to localization of energy primarily in the core, and velocity perturbations cause the energy to be divided between the core and the leading edge. This localization phenomenon does not occur in the sonic-vacuum regime, which yields the surprising result that the energy is no longer contained in strongly nonlinear waves but instead is spread across many sites. In this regime, the exponents are very similar (roughly γ≈1.7 and η≈1) for all three types of disorder and for both types of initial conditions.

Edge fluctuations of limit shapes

In random tiling and dimer models we can get various limit shapes which gives the boundaries between different types of phases. The shape fluctuations at these boundaries give rise to universal limit laws, in particular the Airy process. We survey some models which can be analyzed in detail based on the fact that they are determinantal point processes with correlation kernels that can be computed. We also discuss which type of limit laws that can be obtained.