Lattice Model Research Articles

Solving an internal problem for finite regular two-dimensional lattice spiral elements, excitable plate electromagnetic wave

Background. The work is aimed at developing and researching rigorous methods for solving internal problem of electrodynamics for multi-element structures (metastructures) consisting from the final number of elements, as well as to study the physical processes occurring in them. A special case of such structures are two-dimensional lattices with a fixed interelement distance, consisting of identical elements having the same spatial orientation (regular lattices). Aim. In this work, based on an iterative approach, the internal solution is solved. problems of electrodynamics for a finite regular two-dimensional lattice of spiral elements. In order to obtain a priori information about the electrodynamic characteristics of elements lattice and justification for the choice of projection function systems are analyzed spectral characteristics of the integral operator of the internal problem for a single spiral element. Then the currents on the structure elements are calculated, their spectral characteristics are determined. The results of spectral analysis allow increase the efficiency of solving an internal problem. Methods. The research is based on a strict electrodynamic approach, within the framework of which, for the specified structure in the thin-wire approximation, an integral representation of the electromagnetic field is formed, which, when considered on the surface of conductors together with boundary conditions, is reduced to a system of Fredholm integral equations of the second kind, written relative to unknown current distributions on conductors (internal task). The solution of the internal problem within the framework of the method of moments is reduced to solving a SLAE with a block matrix. Results. A mathematical model of a finite two-dimensional lattice of spiral elements is proposed radiating structure. For the specified structure, in the case of its excitation by a flat electromagnetic wave, based on the iterative approach, the internal problem of electrodynamics was solved. The following were carried out in a wide frequency range: analysis of the convergence of the iterative process, spectral analysis of the integral operator of the internal problem for a single spiral element, as well as spectral analysis of external field and current functions functions on lattice elements. Conclusion. The feasibility of determining the spectral characteristics of integral operators is shown internal task for the elements forming the metastructure. A relationship has been identified between the frequency dependence eigenvalues of the integral operator of the internal problem of single elements, forming a metastructure, with resonance phenomena arising in the metastructure, the influence of resonances on the convergence of the iterative process was confirmed. The feasibility of considering averaged amplitude current spectra is shown. It was revealed that the averaged spectrum of current functions is close to degenerate, especially near resonant frequencies. This allows for use as projection functions a compact set of eigenfunctions that have significant amplitudes in the vicinity of the frequency under study, which significantly simplifies the solution of the internal problem.

Decomposition of nonlinear collision operator in quantum lattice Boltzmann algorithm

Abstract We propose a quantum algorithm to tackle the quadratic nonlinearity in the Lattice Boltzmann (LB) collision operator. The key idea is to build the quantum gates based on the particle distribution functions (PDF) within the coherence time for qubits, and upon quantum state evolution, the resulting PDFs will have quadraticity. To this end, we decompose the collision operator for a DmQn lattice model into a product of 2(n+1) operators, where n is the number of lattice velocity directions. After decomposition, the (n+1) operators with constant entries remain unchanged throughout the simulation, whereas the remaining (n+1) will be built based on the statevector of the previous time step. Also, we show that such a decomposition is not unique. Compared to the second-order Carleman-linearized LB, the present approach reduces the circuit width by half and circuit depth by exponential order. The algorithm has been verified through the one-dimensional flow discontinuity and two-dimensional Kolmogrov-like flow test cases.

A Novel Two-Lane Lattice Model Considering the Synergistic Effects of Drivers’ Smooth Driving and Aggressive Lane-Changing Behaviors

Most existing two-lane traffic flow lattice models fail to fully consider the interactions between drivers’ aggressive lane-changing behaviors and their desire for smooth driving, as well as their combined effects on traffic dynamics. To fill this research gap, under symmetric lane-changing rules, this paper proposes a novel two-lane lattice model that incorporates these two factors as co-influencers. Based on linear and nonlinear stability analyses, we derive the linear stability conditions of the new model, along with the density wave equation and its solutions describing traffic congestion propagation near critical points. Numerical simulations validate the theoretical findings. The results indicate that in the two-lane framework, enhancing either drivers’ lane-changing aggressiveness or introducing the desire for smooth driving alone can somewhat improve traffic flow stability. However, when considering their synergistic effects, traffic flow stability is enhanced more significantly, and the traffic congestion is suppressed more effectively.

Efficient sampling using macrocanonical Monte Carlo and density of states mapping

In the context of Monte Carlo sampling for lattice models, the complexity of the energy landscape often leads to Markov chains being trapped in local optima, thereby increasing the correlation between samples and reducing sampling efficiency. This study proposes a Monte Carlo algorithm that effectively addresses the irregularities of the energy landscape through the introduction of the estimated density of states. This algorithm enhances the accuracy in the study of phase transitions and is not model specific. Although our algorithm is primarily demonstrated on the two-dimensional square lattice model, the method is also applicable to a broader range of lattice and higher-dimensional models. Furthermore, the study develops a method for estimating the density of states of large systems based on that of smaller systems, enabling high-precision density of states estimation within specific energy intervals in large systems without additional sampling. For regions of lower precision, a reweighting strategy is employed to adjust the density of states to enhance the precision further. This algorithm is not only significant within the field of lattice model sampling but may also inspire applications of the Monte Carlo method in other domains. Published by the American Physical Society 2024

Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor ν≤1, bounded below by filling factor ν=1 and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors ν=1 and ν=3. The phases near ν=1 are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands. Published by the American Physical Society 2024

Realizing multiband states with ultracold dipolar quantum simulators

The manipulation of dipolar interactions within ultracold molecular ensembles represents a pivotal advancement in experimental physics, aiming at the emulation of quantum phenomena unattainable through mere contact interactions. Our study uncovers regimes of multiband occupation which allow to probe more realistic, complex long-range interacting lattice models with ultracold dipolar simulators. By mapping out experimentally relevant ranges of potential depths, interaction strengths, particle fillings, and geometric configurations, we calculate the agreement between the state prepared in the quantum simulator and a target lattice state. We do so by separately calculating numerically exact many-body wave functions in the continuous space and single- or multiband lattice representations, and building their many-body state overlaps. Our findings reveal that for shallow lattices and stronger interactions above half filling, multiband population increases, resulting in fundamentally different ground states than the ones observed in simple lowest-band descriptions, e.g., striped vs checkerboard states. A wide range of probed parameter regimes in its turn provides a systematic and quantitative blueprint for realizing multiband states with two-dimensional quantum simulators employing ultracold dipolar molecules. Published by the American Physical Society 2024

Necessity of orthogonal basis vectors for the two-anyon problem in a one-dimensional lattice* *Supported by National Science Foundation of China (Grant Nos. 12074340 and 12474492) and the Science Foundation of Zhejiang Sci-Tech University (Grants No. 20062098-Y, 19062463-Y and 22062344-Y).

Few-body physics for anyons has been intensively studied within the anyon-Hubbard model, including the quantum walk and Bloch oscillations of two-anyon states. Recently, theoretical and experimental simulations of two-anyon states in a one-dimensional lattice have been carried out by expanding the wavefunction in terms of non-orthogonal basis vectors, resulting in non-physical degrees of freedom. In the present work, we deduce finite difference equations for the two-anyon state in a one-dimensional lattice by solving the Schrödinger equation with orthogonal and complete basis vectors. Such an orthogonal scheme gives all the orthogonal physical eigenstates, while the conventional (non-orthogonal) method produces many non-physical redundant eigensolutions whose components violate the anyonic commutation relations. The dynamical property of the two-anyon states in a sufficiently large lattice is investigated and compared in both the orthogonal and conventional schemes. For initial states with two anyons at the same site or two (next-)neighboring sites, we observe the same dynamical behavior in both schemes, including the revival probability, probability density function and two-body correlation. For other initial states, the conventional scheme produces erroneous states that no longer obey the anyonic relations. The period of Bloch oscillations in the pseudo-fermionic limit has been found to be twice that in the bosonic limit, while these oscillations disappear at other statistical parameters. Our findings are vital for quantum simulations of few-body anyonic physics in lattice models.

Exponential growth rate of lattice comb polymers

Abstract We investigate a lattice model of comb polymers and derive bounds on the exponential growth rate of the number of embeddings of
the comb. A comb is composed of a backbone that is a self-avoiding walk and a set of $t$ teeth, also modelled as mutually and self-avoiding walks, attached to the backbone at vertices or nodes of degree 3. Each tooth of the comb has $m_a$ edges and there are $m_b$ edges in the backbone between adjacent degree 3 vertices and between the first and last nodes of degree 3 and the end vertices of degree 1 of the backbone. We are interested in the exponential growth rate as $t \to \infty$ with $m_a$ and $m_b$ fixed. We prove upper bounds on this growth rate and show that for small values of $m_a$ the growth rate is strictly less than that of self-avoiding walks.

Lattice polymers near a permeable interface

Abstract We study the localisation of lattice polymer models near a permeable interface in two dimensions. Localisation can arise due to an interaction between the polymer and the interface, and can be altered by a preference for the bulk solvent on one side or by the application of a force to manipulate the polymer. Different combinations of these three effects give slightly different statistical mechanical behaviours. The canonical lattice model of polymers is the self-avoiding walk which we mainly study with Monte Carlo simulation to calculate the phase diagram and critical phenomena. For comparison, a solvable directed walk version is also defined and the phase diagrams are compared for each case. We find broad agreement between the two models, and most minor differences can be understood as due to the different entropic contributions. In the limit where the bulk solvent on one side is overwhelmingly preferred we see how the localisation transition transforms to the adsorption transition; the permeable interface becomes effectively an impermeable surface.

Quantum phases and transitions in spin chains with non-invertible symmetries

Generalized symmetries often appear in the form of emergent symmetries in low energy effective descriptions of quantum many-body systems. Non-invertible symmetries are a particularly exotic class of generalized symmetries, in that they are implemented by transformations that do not form a group. Such symmetries appear in large families of gapless states of quantum matter and constrain their low-energy dynamics. To provide a UV-complete description of such symmetries, it is useful to construct lattice models that respect these symmetries exactly. In this paper, we discuss two families of one-dimensional lattice Hamiltonians with finite on-site Hilbert spaces: one with (invertible) S_3S3 symmetry and the other with non-invertible \mathsf{Rep}(S_3)𝖱𝖾𝗉(S3) symmetry. Our models are largely analytically tractable and demonstrate all possible spontaneous symmetry breaking patterns of these symmetries. Moreover, we use numerical techniques to study the nature of continuous phase transitions between the different symmetry-breaking gapped phases associated with both symmetries. Both models have self-dual lines, where the models are enriched by so-called intrinsically non-invertible symmetries generated by Kramers-Wannier-like duality transformations. We provide explicit lattice operators that generate these non-invertible self-duality symmetries. We show that the enhanced symmetry at the self-dual lines is described by a 2+1d symmetry-topological-order (SymTO) of type JK_4\boxtimes \overline{JK}_4JK4⊠JK¯4. The condensable algebras of the SymTO determine the allowed gapped and gapless states of the self-dual S_3S3-symmetric and \mathsf{Rep}(S_3)𝖱𝖾𝗉(S3)-symmetric models.

Lattice model for percolation on a plane of partially aligned sticks with length dispersity

Lattice model for percolation on a plane of partially aligned sticks with length dispersity

Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement

Calderbank-Shor-Steane (CSS) codes are a class of quantum error correction codes that contains the toric code and fracton models. A procedure called foliation defines a cluster state for a given CSS code. We use the CSS chain complex and its tensor product with other chain complexes to describe the topological structure in the foliated cluster state, and argue that it has a symmetry-protected topological order protected by generalized global symmetries supported on cycles in the foliated CSS chain complex. We demonstrate the so-called anomaly inflow between CSS codes and corresponding foliated cluster states by explicitly showing the equality of the gauge transformations of the bulk and boundary partition functions defined as functionals of defect world-volumes. We show that the bulk and boundary defects are related via measurement of the bulk system. Further, we provide a procedure to obtain statistical models associated with general CSS codes via the foliated cluster state, and derive a generalization of the Kramers-Wannier-Wegner duality for such statistical models with insertion of twist defects. We also study the measurement-assisted gauging method with cluster-state entanglers for CSS/fracton models based on recent proposals in the literature, and demonstrate a non-invertible fusion of duality operators. Using the cluster-state entanglers, we construct the so-called strange correlator for general CSS/fracton models. Finally, we introduce a new family of subsystem-symmetric quantum models each of which is self-dual under the generalized Kramers-Wannier-Wegner duality transformation, which becomes a non-invertible symmetry.

Time-reversal symmetry breaking in the chemosensory array reveals a general mechanism for dissipation-enhanced cooperative sensing

The Escherichia coli chemoreceptors form an extensive array that achieves cooperative and adaptive sensing of extracellular signals. The receptors control the activity of histidine kinase CheA, which drives a nonequilibrium phosphorylation-dephosphorylation reaction cycle for response regulator CheY. Cooperativity and dissipation are both important aspects of chemotaxis signaling, yet their consequences have only been studied separately. Recent single-cell FRET measurements revealed that kinase activity of the array spontaneously switches between active and inactive states, with asymmetric switching times that signify time-reversal symmetry breaking in the underlying dynamics. Here, we present a nonequilibrium lattice model of the chemosensory array, which demonstrates that the observed asymmetric switching dynamics can only be explained by an interplay between the dissipative reactions within individual core units and the cooperative coupling between neighboring units. Microscopically, the switching time asymmetry originates from irreversible transition paths. The model shows that strong dissipation enables sensitive and rapid signaling response by relieving the speed-sensitivity trade-off, which can be tested by future single-cell experiments. Overall, our model provides a general framework for studying biological complexes composed of coupled subunits that are individually driven by dissipative cycles and the rich nonequilibrium physics within.

Topological phase transitions and flat bands on a square-octagon lattice

We construct a square-octagon lattice model by considering the nearest-neighbor (NN) hoppings with staggered magnetic fluxes and the next-nearest-neighbor (NNN) hoppings, where zero-Chern-number topological insulator (ZCNTI) phases emerge. At 1/4 filling, by tuning the staggered fluxes and NNN hopping potential, this model supports the phase transition from a Chern insulator (CI) with Chern number C = 2 to a ZCNTI phase. At half filling, we observe that staggered magnetic fluxes can induce a higher-order topological insulator (HOTI) state. Interestingly, the ZCNTI appears at 3/4 filling when considering the NN and NNN hoppings in the absence of staggered fluxes, which has been rarely reported in previous work. Contrary to conventional HOTIs, this ZCNTI phase hosts both robust corner states and gapless edge states which can be identified based on the quantized dipole and quadrupole moments. Additionally, a topological flat band (TFB) with flatness ratio about 24 appears. We further investigate ν = 1/2 fractional Chern insulator (FCI) state when hard-core bosons fill into this TFB model.

Multilayer Adsorption Characteristics of CO2 in Organic Nanopores with Different Pore Sizes: Molecular Simulation and Ono-Kondo Lattice Model.

Shale contains numerous organic micropores with significant potential for CO2 storage. To precisely evaluate the CO2 storage potential of shale reservoirs, it is essential to accurately quantify the adsorption of CO2 within these pores. This study used Grand Canonical Monte Carlo (GCMC) molecular simulations to analyze the CO2 adsorption behavior in organic micropores of varying sizes. The study clarified the number and width of the CO2 adsorption layers in micropores of various sizes and proposed a method for segmenting the multilayer adsorption structure. Additionally, the classic Ono-Kondo lattice (OK) model was extended to characterize pore-filling adsorption, incorporating solid-gas and gas-gas interactions. Accurate characterization of CO2 multilayer adsorption and precise calculation of CO2 absolute adsorption in micropores were achieved. Results indicate that CO2 exhibits pore-filling adsorption behavior in organic micropores, forming a multilayer adsorption structure governed by the pore size. Following symmetry principles, the adsorption layer structure in organic micropores can be simplified to a maximum of three layers. When only one adsorption layer forms, its width equals the gas-accessible pore size. For two or more layers, the width of the original layer stabilizes as additional layers form. The stable adsorption layer widths, from nearest to farthest from the pore wall, are 0.33, 0.45, and 0.39 nm. The improved OK model accurately describes CO2 excess and absolute adsorption isotherms across different pore sizes and calculates the CO2 density in each adsorption layer, showing high consistency with GCMC simulation results. These findings highlight the importance of understanding the CO2 multilayer adsorption structure for accurately estimating CO2 adsorption in organic micropores.

Boundary excitation of nonlinearly modulated bending strain waves in a metamaterial

A non-linear modulation of bending waves in a metamaterial mass-in-mass lattice model is studied. Various kinds of non-linear wave modulation are obtained using a harmonic boundary excitation. It is shown, that these waves can be described by an asymptotic simplification of the equations of motion resulting in a non-linear modulation equation for the displacements. Exact periodic traveling wave solutions to the equation demonstrate a dependence on the sign of the equation coefficients or the elastic parameters of the original model. Dispersion relation for the carrier part of the solution is obtained as a function of wave number versus frequency, it is found how its solutions relate to the acoustic and optic branches and the band gap. This form of the dispersion relation is further used for a description of numerical results on the wave modulation by a harmonic boundary excitation.

A GPU-Based Lattice Boltzmann Method for Predicting Near- and Far-Field Jet Noise

Jet flow and noise are simulated using the lattice Boltzmann method (LBM). The D3Q19 lattice model calculates the flow field with a high-order distribution function to overcome LBM limitations in solving high Mach number flows. Multiple relaxation times (MRT) and large eddy simulation (LES) are used in this study. Compressible LBM was applied to the simulation jet flow to demonstrate the ability of the fifth-order equilibrium distribution function to simulate compressible flows efficiently. The results from the LBM simulation were then employed in Kirchhoff's surface integral approach to predict far-field jet noise. In this research, we used the compute unified device architecture (CUDA) to implement the LBM in a graphics processing unit (GPU), thus creating a hybrid code, LBM-MRT-LES. The obtained results agreed with the experimental and numerical results in the literature.

A multi-layer multi-configurational time-dependent Hartree approach to lattice models beyond one dimension.

The multi-layer multi-configurational time-dependent Hartree (MCTDH) approach is an efficient method to study quantum dynamics in real and imaginary time. The present work explores its potential to describe quantum fluids. The multi-layer MCTDH approach in second quantization representation is used to study lattice models beyond one dimension at finite temperatures. A scheme to map the lattice sites onto the MCTDH tree representation for multi-dimensional lattice models is proposed. A statistical sampling scheme previously used in MCTDH calculations is adapted to facilitate an efficient description of the thermal ensemble. As example, a two-dimensional hard-core Bose-Hubbard model is studied considering up to 64 × 64 lattice sites. The single particle function basis set size required to obtain converged results is found to not increase with the lattice size. The numerical results properly simulate the finite temperature Berezinskii-Kosterlitz-Thouless phase transition.

A lattice fraction stress model with consideration of thermal activation

A lattice fraction stress model with consideration of thermal activation

Initial Growth of the Pentacene Monolayer on a Si(001)-2 × 1 Substrate: A Lattice Model View

Initial Growth of the Pentacene Monolayer on a Si(001)-2 × 1 Substrate: A Lattice Model View