Two-dimensional Lattice Model Research Articles

Two-dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method

Two-dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method

ЕЛЕКТРОФІЗИЧНІ ПРОЦЕСИ У КОМПОЗИТНИХ НАПІВПРОВІДНИХ ЕКРАНАХ ТА ЇХНІЙ ВПЛИВ НА ДІЕЛЕКТРИЧНІ ПАРАМЕТРИ СИЛОВИХ ВИСОКОВОЛЬТНИХ КАБЕЛІВ

The methodology for modelling the percolation process in semiconductor shields of power high-voltage cables is proposed. The semiconductor screen is represented by a two-dimensional lattice model with a polymer matrix filled with conductive carbon black particles. Model matrix's of the composite, depending on the probability of filling and the concentration of the conductive filler, agree with micrographs of the distribution of soot in the polyethylene matrix of the semiconducting screen of the power cable. Taking into account the stochastic of the percolation process, the concentration range of the conductive filler, which determines the flow threshold in the presented model, was determined. Disturbances are observed on the experimental time dependence of the absorption current of the power cable, which is indirect evidence of the accumulation of surface charges at the interface between the semiconductor screen and high-voltage polymer insulation. The time dependences of the electric capacity and the tangent of the dielectric loss angle at a frequency of 120 Hz confirm the stochastic nature of the process of accumulation of surface charges. This process causes a time-delayed interphase polarization in power high-voltage cables. References 36, figure 5.

On different approaches to integrable lattice models

Interaction-round the face (IRF) models are two-dimensional lattice models of statistical mechanics defined by an affine Lie algebra and admissibility conditions depending on a choice of representation of that affine Lie algebra. Integrable IRF models, i.e. the models the Boltzmann weights of which satisfy the quantum Yang–Baxter equation, are of particular interest. In this paper, we investigate trigonometric Boltzmann weights of integrable IRF models. By using an ansatz proposed by one of the authors in some previous works, the Boltzmann weights of the restricted IRF models based on the affine Lie algebras su(2)k and su(3)k are computed for fundamental and adjoint representations for some fixed levels k. New solutions for the Boltzmann weights are obtained. We also study the vertex-IRF correspondence in the context of an unrestricted IRF model based on su(3)k (for general k) and discuss how it can be used to find Boltzmann weights in terms of the quantum R^ matrix when the adjoint representation defines the admissibility conditions.

Amino acid chiral amplification using Monte Carlo dynamic.

This study investigates the stability of chiral-molecule solution phases, with a specific focus on amino acids. The model framework is based on a two-dimensional square lattice model, where individual sites may be occupied by oriented chiral molecules or structureless solvent particles. Utilizing the Glauber dynamics and statistical mechanical formalism, as previously introduced and examined by Lombardo et al., we explore the influence of temperature, amino acid concentration, enantiomeric excess, and homochiral interaction strength on nucleation mechanisms, equilibrium phase behavior, and crystal composition. Our findings offer thermodynamic insights into the chiral amplification process of amino acids, contributing to a deeper understanding of the underlying processes.

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.

Machine learning renormalization group for statistical physics

We develop a machine-learning renormalization group (MLRG) algorithm to explore and analyze many-body lattice models in statistical physics. Using the representation learning capability of generative modeling, MLRG automatically learns the optimal renormalization group (RG) transformations from self-generated spin configurations and formulates RG equations without human supervision. The algorithm does not focus on simulating any particular lattice model but broadly explores all possible models compatible with the internal and lattice symmetries given the on-site symmetry representation. It can uncover the RG monotone that governs the RG flow, assuming a strong form of the c-theorem. This enables several downstream tasks, including unsupervised classification of phases, automatic location of phase transitions or critical points, controlled estimation of critical exponents, and operator scaling dimensions. We demonstrate the MLRG method in two-dimensional lattice models with Ising symmetry and show that the algorithm correctly identifies and characterizes the Ising criticality.

Subsystem non-invertible symmetry operators and defects

We explore non-invertible symmetries in two-dimensional lattice models with subsystem \mathbb Z_2ℤ2 symmetry. We introduce a subsystem \mathbb Z_2ℤ2-gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers-Wannier transformation. The corresponding duality operators and defects are constructed by gaugings on the whole or half of the Hilbert space. By gauging twice, we derive fusion rules of duality operators and defects, which enriches ordinary Ising fusion rules with subsystem features. Subsystem Kramers-Wannier duality defects are mobile in both spatial directions, unlike the defects of invertible subsystem symmetries. We finally comment on the anomaly of the subsystem Kramers-Wannier duality symmetry, and discuss its subtleties.

Enhanced nematicity emerging from higher-order Van Hove singularities

Motivated by the experimental identification of a higher-order Van Hove singularity (VHS) in $A{\text{V}}_{3}{\mathrm{Sb}}_{5}$ kagome metals, we study electronic instabilities of two-dimensional lattice models with higher-order VHS and flavor degeneracy. In contrast to conventional VHSs, the larger power-law density of states and the weaker nesting propensity of higher-order VHSs conspire together to generate distinct competing instabilities. After discussing the occurrence of higher-order VHSs on square and kagome lattice models, we perform unbiased renormalization group calculations to study competing instabilities and find a rich phase diagram containing ferromagnetism, antiferromagnetism, superconductivity, and Pomeranchuk orders. Remarkably, there is a generic transition from superconductivity to a $d$-wave Pomeranchuk order with increasing flavor number. Implications for the intriguing quantum states of $A{\text{V}}_{3}{\mathrm{Sb}}_{5}$ kagome metals are also discussed.

Application of artificial neural networks for modeling of electronic excitation dynamics in 2D lattice: Direct and inverse problems

Machine learning (ML) approaches are attracting wide interest in the chemical physics community since a trained ML system can predict numerical properties of various molecular systems with a small computational cost. In this work, we analyze the applicability of deep, sequential, and fully connected neural networks (NNs) to predict the excitation decay kinetics of a simple two-dimensional lattice model, which can be adapted to describe numerous real-life systems, such as aggregates of photosynthetic molecular complexes. After choosing a suitable loss function for NN training, we have achieved excellent accuracy for a direct problem—predictions of lattice excitation decay kinetics from the model parameter values. For an inverse problem—prediction of the model parameter values from the kinetics—we found that even though the kinetics obtained from estimated values differ from the actual ones, the values themselves are predicted with a reasonable accuracy. Finally, we discuss possibilities for applications of NNs for solving global optimization problems that are related to the need to fit experimental data using similar models.

Application of the dynamic Monte Carlo method to pedestrian evacuation dynamics

In this study, we investigate a two-dimensional lattice model for crowd evacuation dynamics by using a dynamic Monte Carlo (DMC) method. This model is built on the microscopic Arrhenius dynamics along with the exclusion rule in which stochastic processes govern the individual movements depending on the relative distance to the room exit. Even though individual decision-making procedures can be complicated during the evacuation in an emergency, our model can quantitatively estimate the time for them to evacuate and predict the emerging patterns of the crowds during the process. The results exhibit the phenomena such that pedestrians spontaneously gather at the exit and form an arched shape close to the door. The DMC simulations and observations agree with the corresponding study in the literature. The DMC algorithm is computationally efficient due to its major property —“rejection-free”, which makes it a suitable tool to simulate evacuation dynamics for a large group of pedestrians.

Realization of the topological Hopf term in two-dimensional lattice models

It is known that a two-dimensional spin system can acquire a topological Hopf term by coupling to massless Dirac fermions whose energy spectrum has a single cone. But it is challenging to realize the Hopf term in condensed matter physics due to the fermion-doubling in the low-energy spectrum. In this work we propose a scenario to realize the Hopf term in lattice models. The central aim is tuning the coupling between the spins and the Dirac fermions such that the topological terms contributed by the two cones do not cancel each other. To this end, we consider $p_x$ and $p_y$ orbitals for the Dirac fermions on the honeycomb lattice such that there are totally four bands. By utilizing the orbital degrees of freedom, a $\theta=2\pi$ Hopf term is successfully generated for the spin system after integrating out the Dirac fermions. If the fermions have a small gap $m_0$ or if the spin-orbit coupling is considered, then $\theta$ is no longer quantized, but it may flow to multiple of $2\pi$ under renormalization. The ground state and the physical response of a spin system having the Hopf term are discussed.

Lattice Folding Simulation of Peptide by Quantum Computation

Computational protein folding has attracted considerable interest over the years, including molecular simulations and artificial intelligence assisted methods. On the other hand, research and development of quantum computer hardware and software have been thriving recently. In this paper, we report a case study of peptide (PSVKMA) folding based on a two-dimensional lattice model, by using both the blueqat quantum simulator (called AutoQML) and the IonQ quantum device. As a result, it was found that the actual device was still susceptible to noises.

A two-dimensional stochastic fractional non-local diffusion lattice model with delays

The well-posedness, regularity and general stability of solutions to a two-dimensional stochastic non-local delay diffusion lattice system with a time Caputo fractional operator of order [Formula: see text] are investigated in [Formula: see text] spaces for [Formula: see text]. First, the global existence and uniqueness of solutions are established by using a temporally weighted norm, the Burkholder–Davis–Gundy inequality and the Banach fixed point theorem. Then the continuous dependence of solutions on initial values is established in the sense of [Formula: see text]th moment. In particular, the [Formula: see text]th moment Hölder regularities in time and [Formula: see text]th moment general stability, including polynomial and logarithmic stability of solutions, are obtained.

The cavity method to protein design problem

In this study, we propose an analytic statistical mechanics approach to solve a fundamental problem in biological physics called protein design. Protein design is an inverse problem of protein structure prediction, and its solution is the amino acid sequence that best stabilizes a given conformation. Despite recent rapid progress in protein design using deep learning, the challenge of exploring protein design principles remains. Contrary to previous computational physics studies, we used the cavity method, an extension of the mean-field approximation that becomes rigorous when the interaction network is a tree. We found that for small two-dimensional lattice hydrophobic-polar protein models, the design by the cavity method yields results almost equivalent to those from the Markov chain Monte Carlo method with lower computational cost.

Dirac fermions with plaquette interactions. II. SU(4) phase diagram with Gross-Neveu criticality and quantum spin liquid

At sufficiently low temperatures, interacting electron systems tend to develop orders. Exceptions are quantum critical point (QCP) and quantum spin liquid (QSL), where fluctuations prevent the highly entangled quantum matter to an ordered state down to the lowest temperature. While the ramification of these states may have appeared in high-temperature superconductors, ultra-cold atoms, frustrated magnets and quantum Moir\'e materials, their unbiased presence remain elusive in microscopic two-dimensional lattice models. Here, we show by means of large-scale quantum Monte Carlo simulations of correlated electrons on the $\pi$-flux square lattice subjected to extended Hubbard interaction, that a Gross-Neveu QCP separating massless Dirac fermions and an columnar valence bond solid at finite interaction, and a possible Dirac QSL at the infinite yet tractable interaction limit emerge in a coherent sequence. These unexpected novel quantum states resides in this simple-looking model, unifying ingredients including emergent symmetry, deconfined fractionalization and the dynamic coupling between emergent matter and gauge fields, will have profound implications both in quantum many-body theory and understanding of the aforementioned experimental systems.

Magnon-ferron coupling mediated by dynamical Dzyaloshinskii-Moriya interaction in a two-dimensional multiferroic model

In this work, we employ a two-dimensional square lattice model hosting both magnetic and ferroelectric orders to analyze the role of the Dzyaloshinskii-Moriya interaction in the ground state configuration and quasiparticle excitations. The inverse Dzyaloshinskii-Moriya mechanism stabilizes a spin spiral accompanying an enhanced ferroelectric polarization. As the bosonic excitations of the magnetic and ferroelectric orders, magnons and ferrons are coupled via the dynamical Dzyaloshinskii-Moriya interaction. We derive explicitly the magnon-ferron coupling and investigate the resulting magnon-ferron hybridization in different spin-textured phases driven by an external magnetic field, from which a field-associated nonreciprocal magnon-ferron coupling is predicted in the spin conical phase.

TeNeS: Tensor network solver for quantum lattice systems

TeNeS (Tensor Network Solver) [1,2] is a free/libre open-source software program package for calculating two-dimensional many-body quantum states based on the tensor network method and the corner transfer matrix renormalization group (CTMRG) method. This package calculates ground-state wavefunctions for user-defined Hamiltonians and evaluates user-defined physical quantities such as magnetization and correlation functions. For certain predefined models and lattices, there is a tool that makes it easy to generate input files. TeNeS uses an OpenMP/MPI hybrid parallelized tensor operation library and thus can perform large-scale calculations using massively parallel machines. Program summaryProgram Title: TeNeSCPC Library link to program files:https://doi.org/10.17632/psm26xxbvd.1Code Ocean capsule:https://codeocean.com/capsule/1510058Licensing provisions: GNU General Public License version 3Programming language:C++ and python3External routines/libraries: mptensorNature of problem: TeNeS calculates the approximate ground states and their properties of user-defined two-dimensional quantum lattice models using user-friendly input files. Numerically exact solutions of such tasks generally require an exponentially diverging computational time, whereas the error in the output of TeNeS is well controlled and can be reduced with a polynomial cost.Solution method: TeNeS implements the tensor networks method based on a tensor-product-state (TPS) wavefunction and the corner transfer matrix renormalization group method. TeNeS also supports massively parallel computing using the library mptensor, which implements OpenMP/MPI hybrid parallelized tensor operations.

Thermoelectric transport of type-I, II, and III massless Dirac fermions in a two-dimensional lattice model

We study longitudinal electric and thermoelectric transport coefficients of Dirac fermions on a simple lattice model where tuning of a single parameter enables us to change the type of Dirac cones from type-I to type-II. We pay particular attention to the behavior of the critical situation, i.e., the type-III Dirac cone. We find that the transport coefficients of the type-III Dirac fermions behave as the limiting case of neither the type-I nor type-II. On the one hand, the qualitative behaviors of the type-III case are similar to those of the type-I case. On the other hand, the transport coefficients do not change monotonically upon increasing the tilting; namely, the largest thermoelectric response is obtained not for the type-III case but for the optimally tilted type-I case. For the optimal case, the sizable transport coefficients are obtained; for example, the dimensionless figure of merit is 0.18.

Perfect state transfer in two dimensions and the bivariate dual-Hahn polynomials

Abstract A new solvable two-dimensional spin lattice model defined on a regular grid of triangular shape is proposed. The hopping amplitudes between sites are related to recurrence coefficients of certain bivariate dual-Hahn polynomials. For a specific choice of the parameters, perfect state transfer and fractional revival are shown to take place.

Ionic liquids in conducting nanoslits: how important is the range of the screened electrostatic interactions?

Analytical models for capacitive energy storage in nanopores attract growing interest as they can provide in-depth analytical insights into charging mechanisms. So far, such approaches have been limited to models with nearest-neighbor interactions. This assumption is seemingly justified due to a strong screening of inter-ionic interactions in narrow conducting pores. However, how important is the extent of these interactions? Does it affect the energy storage and phase behavior of confined ionic liquids? Herein, we address these questions using a two-dimensional lattice model with next-nearest and further neighbor interactions developed to describe ionic liquids in conducting slit confinements. With simulations and analytical calculations, we find that next-nearest interactions enhance capacitance and stored energy densities and may considerably affect the phase behavior. In particular, in some range of voltages, we reveal the emergence of large-scale mesophases that have not been reported before but may play an important role in energy storage.