Lattice Model Research Articles

Universal scaling relations for growth phenomena

The Family–Vicsek (FV) relation is a seminal universal relation obtained for the global roughness at the interface of two media in the growth process. In this work, we revisit the scaling analysis and, through both analytical and computational means, show that the FV relation can be generalized to a new scaling independent of the size, substrate dimension d, and scaling exponents. We use the properties of lattice growth models in the Kardar–Parisi–Zhang and Villain–Lai–Das Sarma universality classes for 1⩽d⩽3 to support our claims.

Theoretical insights into the interplay between metal-organic and covalent bonding in single-layer molecular networks formed by halogen dissociation.

Synthesis via dehalogenative coupling due to thermal annealing is one of the most common routes of growing metal-organic and covalent polymer networks on catalytic metal surfaces. We present a computational approach taking into account both metal-coordinated and covalent C-C bonding interactions, which drive the self-assembly of tetrabrominated polyarene molecules into single-layer ordered and disordered nanostructures. The proposed coarse-grained lattice model is simulated using the Monte Carlo method. We investigate the annealing effect in ensembles of nearly and fully dehalogenated molecules, accordingly decreasing the concentration of dissociated (chemisorbed) halogen atoms, to account for the desorption process. The results suggest that dissociated halogens may be at least partially responsible for fragmentation of metal-organic networks on the Cu and Au surfaces. The simulations also show that fragmented covalent networks are mostly disordered or characterized by short-range glass-like order, but larger domains of these phases can be obtained after removing the split off Br atoms. We additionally examine the potential formation of fragments with a hybrid structure consisting of oligomer chains linked side-to-side by metal adatoms.

On the notion of strong correlation in electronic structure theory.

Strong correlation has been said to have many faces, and appears to have many synonyms of questionable suitability. In this work we aim not to define the term once and for all, but to highlight one possibility that is both rigorously defined and physically transparent, and remains so in reference to molecules and quantum lattice models. We survey both molecular examples - hydrogen systems (Hn, n = 2, 4, 6), Be2, H-He-H, and benzene - and the half-filled Hubbard model over a range of correlation regimes. Various quantities are examined including the extent of spin symmetry breaking in correlated single-reference wave functions, energetic ratios inspired by the Hubbard model and the Virial theorem, and metrics derived from the one- and two-electron reduced density matrices (RDMs). The trace and the square norm of the cumulant of the two-electron reduced density matrix capture what may well be defined as strong correlation. Accordingly, strong correlation is understood as a statistical dependence between two electrons, and is distinct from the concepts of "correlation energy" and more general than entanglement quantities that require a partitioning of a quantum system into distinguishable subspaces. This work enables us to build a bridge between a rigorous and quantifiable regime of strong electron correlation and more familiar chemical concepts such as anti-aromaticity in the context of Baird's rule.

A multivariate method of forecasting the nonlinear dynamics of production network based on multilayer neural models

Design of production network based on multilayer neural models is considered in this paper. Design of production network is crucial because it determines the optimal location of production and logistics facilities, affects cost efficiency, customer service level and overall competitiveness in the global market. Multi-layer neural networks play an important role in this process, using advanced algorithms, machine learning models and optimization techniques to analyze huge amounts of data. Special attention is focused on qualitative analysis of dynamic behavior, dynamic lattice model. The model includes rate constants and initial conditions affecting the model trajectories, which can be classified as a stable site, limit cycle, or chaotic attractor. We aim to solve the problem of qualitative behavior of the model as a problem of multilayer neural models. A multivariate method of predicting nonlinear dynamics was used to construct the training data set. Neural networks defined by regenerative architectures with linear and non-linear outputs were analyzed and compared. As a result of the analysis, it was found that architectures with linear outputs show better correspondence between expected and predicted values. Architectures with non-linear outputs, despite their complexity, exhibit less accuracy and more deviation compared to linear ones. The single-layer architecture with linear outputs shows the best accuracy, although the two-layer architecture with linear outputs has the lowest rms error. Architectures with non-linear outputs have faster training times but poor accuracy, while architectures with linear outputs require more training time but have lower errors. The results obtained in the work indicate the importance of choosing the right architecture of the neural network depending on the tasks and requirements for accuracy and training time of the model.

Real-space model for activated processes in rejuvenation and memory behavior of glassy systems.

We offer an alternative real-space description, based purely on activated processes, for the understanding of relaxation dynamics in hierarchical landscapes. To this end, we use the cluster model, a coarse-grained lattice model of a jammed system, to analyze rejuvenation and memory effects during aging after a hard quench. In this model, neighboring particles on a lattice aggregate through local interactions into clusters that fragment with a probability based on their size. Despite the simplicity of the cluster model, it has been shown to reproduce salient observables of the aging dynamics in colloidal systems, such as those accounting for particle mobility and displacements. Here, we probe the model for more complex quench protocols and show that it exhibits rejuvenation and memory effects similar to those attributed to the complex hierarchical structure of a glassy energy landscape.

Periodic measures for a neural field lattice model with state dependent superlinear noise

Periodic measures for a neural field lattice model with state dependent superlinear noise

Surface mobility gradient and emergent facilitation in glassy films.

Confining glassy polymers into films can substantially modify their local and film-averaged properties. We present a lattice model of film geometry with void-mediated facilitation behaviors but free from any elasticity effect. We analyze the spatially varying viscosity to delineate the transport properties of glassy films. The film mobility measurements reported by Yang et al., Science, 2010, 328, 1676 are successfully reproduced. The flow exhibits a crossover from a simple viscous flow to a surface-dominated regime as the temperature decreases. The propagation of a highly mobile front induced by the free surface is visualized in real space. Our approach provides a microscopic treatment of the observed glassy phenomena.

Dark Matter and Dark Energy from Lattice Model of Universe

Dark Matter and Dark Energy from Lattice Model of Universe

Twistronics of Kekulé Graphene: Honeycomb and Kagome Flat Bands.

Kekulé-O order in graphene, which has recently been realized experimentally, induces Dirac electron masses on the order of m∼100 meV. We show that twisted bilayer graphene in which one or both layershave Kekulé-O order exhibits nontrivial flat electronic bands on honeycomb and kagome lattices. When only one layer has Kekulé-O order, there is a parameter regime for which the lowest four bands at charge neutrality form an isolated two-orbital honeycomb lattice model with two flat bands. The bandwidths are minimal at a magic twist angle θ≈0.7° and Dirac mass m≈100 meV. When both layers have Kekulé-O order, there is a large parameter regime around θ≈1° and m≳100 meV in which the lowest three valence and conduction bands at charge neutrality each realize isolated kagome lattice models with one flat band, while the next three valence and conduction bands are flat bands on triangular lattices. These flat band systems may provide a new platform for strongly correlated phases ofmatter.

A lattice model based on percolation theory for cold atmospheric DBD plasma decontamination kinetics

The tailing phenomenon, where the survival curve of bacteria shows a slow tailing period after a rapid decline, is a ubiquitous inactivation kinetics process in the advanced plasma sterilization field. While classical models suggest that bacterial resistance dispersion causes the tailing phenomenon, experiments suggest that the non-uniform spatial distribution of spores (clustered structure) is the cause. However, no existing inactivation kinetics model can accurately describe spatial heterogeneity. In this paper, we propose a lattice model based on percolation theory to explain the inactivation kinetics by considering the non-uniform spatial distribution of spores and plasma. Our model divides spores into non-clustered and clustered types and distinguishes between short-tailing and long-tailing compositions and their formation mechanisms. By systematically studying the effects of different spore and plasma parameters on the tailing phenomenon, we provide a reasonable explanation for the kinetic law of the plasma sterilization survival curve and the mechanism of the tailing phenomenon in various cases. As an example, our model accurately explains the 80-second kinetics of atmospheric pressure plasma inactivation of spores, a process that previous models struggled to understand due to its multi-stage and long-tail phenomena. Our model predicts that increasing the spatial distribution probability of plasma can shorten the complete killing time under the same total energy, and we validate this prediction through experiments. Our model successfully explains the seemingly irregular plasma sterilization survival curve and deepens our understanding of the tailing phenomenon in plasma sterilization. This study offers valuable insights for the sterilization of food surfaces using plasma technology, and could serve as a guide for practical applications.

A discrete lattice model with axial and angular springs for modeling fracture in fiber-reinforced composite laminates

In this research, we developed a new 2D triangular lattice model with axial and angular springs to simulate fracture problems in composites. The inclusion of angular springs in the model formulation resolves the constraint related to the choice of the shear modulus, which is present in other lattice models that only consider axial springs. Moreover, it accounts for progressive damage in composites by effectively integrating a linear softening constitutive law. This model is based on equating the strain energy stored in a representative hexagonal cell to its corresponding continuum solid. Four numerical examples demonstrate the ability of this method to predict elastic constants and dynamic and quasi-static fracture problems in unidirectional composites. The results will be compared with the numerical and empirical results documented by the other researchers.

Integrative modeling of JCVI-Syn3A nucleoids with a modular approach

A lattice-based method is presented for creating 3D models of entire bacterial nucleoids integrating ultrastructural information cryoelectron tomography, genomic and proteomic data, and experimental atomic structures of biomolecules and assemblies. The method is used to generate models of the minimal genome bacterium JCVI-Syn3A, producing a series of models that test hypotheses about transcription, condensation, and overall distribution of the genome. Lattice models are also used to generate atomic models of an entire JCVI-Syn3A cell.

Critical line of the triangular Ising antiferromagnet in a field from a C_{3}-symmetric corner transfer matrix algorithm.

The corner transfer matrix renormalization group (CTMRG) algorithm has been extensively used to investigate both classical and quantum two-dimensional (2D) lattice models. The convergence of the algorithm can strongly vary from model to model depending on the underlying geometry and symmetries, and the presence of algebraic correlations. An important factor in the convergence of the algorithm is the lattice symmetry, which can be broken due to the necessity of mapping the problem onto the square lattice. We propose a variant of the CTMRG algorithm, designed for models with C_{3}-symmetry, which we apply to the conceptually simple yet numerically challenging problem of the triangular lattice Ising antiferromagnet in a field, at zero and low temperatures. We study how the finite-temperature three-state Potts critical line in this model approaches the ground-state Kosterlitz-Thouless transition driven by a reduced field (h/T). In this particular instance, we show that the C_{3}-symmetric CTMRG leads to much more precise results than both existing results from exact diagonalization of transfer matrices and Monte Carlo.

Conformal Field Theory Ground States as Critical Points of an Entropy Function.

We derive an entropy formula satisfied by the ground states of 1+1D conformal field theories. The formula implies that the ground state is the critical point of an entropy function. We conjecture that this formula may serve as an information-theoretic criterion for conformal field theories, which differs from the conventional algebraic definition. In addition to these findings, we use the same proof method to extract the six global conformal generators of the conformal field theory from its ground state. We validate our results by testing them on different critical lattice models, with excellent agreement.

Berry-Curvature Engineering for Nonreciprocal Directional Dichroism in Two-Dimensional Antiferromagnets.

In two-dimensional antiferromagnets, we find that the mixed Berry curvature can be attributed as the geometrical origin of the nonreciprocal directional dichroism (NDD), which refers to the difference in light absorption between opposite propagation directions. This Berry curvature is closely related to the uniaxial strain in accordance with the symmetry constraint, leading to a highly tunable NDD, whose sign and strength can be tuned via strain direction. We choose the lattice model of MnBi_{2}Te_{4} as a concrete example. The coupling between mixed Berry curvature and strain also suggests the magnetic quadrupole of the Bloch wave packet as the macroscopic order parameter probed by the NDD in two dimensions, which is distinct from the multiferroic order P×M or the spin toroidal and quadrupole order within a unit cell in previous studies. Our work paves the way for the Berry-curvature engineering for optical nonreciprocity in two-dimensional antiferromagnets.

Dynamics of charge imbalance resolved negativity after a local joining quench

In this paper, we consider the dynamics of charge imbalance resolved negativity after a local joining quench in the 1 + 1 dimensional free complex boson CFT. In the first part, we study the local joining quench by applying conformal maps, obtaining analytical universal results. We first calculate the quench dynamics of charged logarithmic negativity. Then using the Fourier transformation, we obtain the charge imbalance resolved negativity. The total negativity can be recovered from the charge-resolved ones. In the second part, we test our CFT predictions against the underlying lattice model numerically. Finally, we explain our results based on the quasi-particle picture.

TT¯ Deformation: A Lattice Approach

Integrable quantum field theories can be regularized on the lattice while preserving integrability. The resulting theories on the lattice are integrable lattice models. A prototype of such a regularization is the correspondence between a sine-Gordon model and a six-vertex model on a light-cone lattice. We propose an integrable deformation of the light-cone lattice model such that in the continuum limit we obtain the TT¯-deformed sine-Gordon model. Under this deformation, the cut-off momentum becomes energy dependent and the underlying Yang–Baxter integrability is preserved. Therefore, this deformation is integrable but non-local: similar to the TT¯ deformation of quantum field theory.

NUMERICAL SIMULATION OF DYNAMICS OF BLOCK MEDIA BY MOVABLE LATTICE AND MOVABLE AUTOMATA METHODS

Two versions of modified Burridge-Knopoff model including state dependent friction, elastic force and thermal conductivity are derived. The friction model describes a velocity weakening of friction and elasticity between moving blocks and an increase of both static friction and rigidity during stick periods as well their weakening during motion. It provides a simplified but qualitatively correct behavior including the transition from smooth sliding to stick-slip behavior, which is often observed in various tribological and tectonic systems. Attractor properties of the model dynamics is studied also. The alternative versions of the model are proposed which apply a simulation of the motion of interacting elastically connected mesh elements and motion of relatively large solid blocks, utilizing technique of the movable cellular automata. First version of the model was already basically studied before. Its advanced version here involves all components of the real system: state-depending friction and changeable rigidity, as well as heat production and thermal conductivity. Model based on the movable automata also involves the components included into traditional lattice model. It has its own ad-vantages and disadvantages which are also discussed in the paper.

Novel insight into the physics of short-range ordered nanoholes: Newly defined lattice model and transmittance response related to lattice parameters and ordering evolution

This paper presents unforeseen conceptualization, methods and results on the physics of short-range ordered (SRO) gold nanohole (NH) distributions, fabricated by a recent protocol developed by the authors. The straightforward extension to SRONHs of the existing knowledge about periodic NH arrays is confuted and an alternative interpretative picture is proposed and discussed based on three main advancements. First, it is set up a so-called short-range lattice (SR-Lat) method to rigorously and fully characterize the coverage-dependent short-range ordering through the determination of local coordination and periodicity length (aSR) of the NH arrangement. Second, it is demonstrated the failure of the common assumption that the average center-to-center distance of nearest neighbor colloids/nanoholes (dNN) is the characteristic length-scale of SRONHs and aSR is set as the proper periodicity parameter. Third, a predictive relationship is formulated between the wavelength of the propagating plasmon modes and aSR that highlights inherent differences with respect to periodic NHs.The presented results lay rigorous foundation for studying systems with correlated diosrdering in general and for making predictions useful not only in design and applications of SRONHs, but also on the surface physics in the photonics and sensing fields.

Transition to chaos in extended systems and their quantum impurity models

Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the Tavis–Cummings model on a finite chain. By studying level-spacing statistics, adjacent gap ratios, and spectral form factors, we observe the transition from integrability to chaos as the hopping between the Tavis–Cummings sites is increased above a finite value. The results are obtained by means of exact numerical diagonalization which becomes notoriously hard for extended lattice geometries. In an attempt to circumvent these difficulties, we identify a minimal single-site quantum impurity model that successfully captures the spectral properties of the lattice model. This approach is intended to be adaptable to other lattice models with large local Hilbert spaces.