Two-dimensional Lattice Model Research Articles

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

Emergence and evolution of electronic modes with temperature in spin-gapped Mott and Kondo insulators

Electronic modes emerge within the band gap at nonzero temperature in strongly correlated insulators such as Mott and Kondo insulators, exhibiting momentum-shifted magnetic dispersion relations from the band edges. As the temperature increases, the emergent modes gain considerable spectral weights and form robust bands that differ from the zero-temperature bands. Here, the origin of the emergent modes, their relation to doping-induced modes, and how their spectral weights increase with temperature are clarified in the ladder and bilayer Hubbard models and one- and two-dimensional Kondo lattice models using effective theory for weak inter-unit-cell hopping and numerical calculations. The results indicate that the temperature-driven change in the band structure reflecting spin excitation, including the change in the number of bands, can be observed in various strongly correlated insulators even with a spin gap, provided that the temperature increases up to about spin-excitation energies. The controlled analyses developed in this study significantly contribute to the fundamental understanding of the band structure of strongly correlated insulators at nonzero temperature. Published by the American Physical Society 2024

Emerging topological multiferroics from the 2D Rice-Mele model

We introduce a two-dimensional dimerized lattice model that reveals a remarkable feature: the emergence of a complex, non-trivial topological multiferroic phase marked by zero Berry curvature and a significant Berry connection that influences the model’s bulk topology. This model extends the one-dimensional Rice-Mele Hamiltonian model to explore polarization-dependent topological properties in a 2D Su-Schrieffer-Heeger lattice, providing a detailed framework for studying the impact of symmetry-breaking and spatially varying potentials on electronic and spin properties. The findings are particularly relevant for spintronics, offering a foundation for topologically robust and electrically controlled spin-conducting edge states, with implications for developing advanced spin-dependent transport devices.

Copper(II) salts and complexes of 2-amino-5-nitropyridine*

Four new copper compounds of 2-amino-5-nitropyridine/pyridinium (5NAP/5NAPH) have been prepared and characterized: (5NAPH)2[CuBr4], 2; (d2-5NAPD)2[CuBr4], 2a; (5NAP)2CuCl2, 3; (5NAP)2CuBr2, 4. Compounds 2 and 2a are isomorphous and crystallize in the triclinic space group P-1. Packing is stabilized by hydrogen/deuterium bonds. Short Br…Br contacts provide potential magnetic superexchange pathways, but only very weak antiferromagnetic exchange is observed (J/kB∼-2 K). Compounds 3 and 4 are also isomorphous and crystallize in the monoclinic space group P21/c. The molecules are linked into chains by bihalide bridges, and the chains linked into rectangular/square layers by short X…X. contacts. Variable temperature magnetic data were best fit by the S = ½ antiferromagnetic rectangular model for 3 (C = 0.429(1) emu-K/mol-Oe, J/kB = −9.38(6) K, J’/kB = −5.91(4) K). Variable temperature magnetic susceptibility data for 4 were best fit by the two-dimensional antiferromagnetic square lattice model (C = 0.43(1) emu-K/mol-Oe, J/kB = −36.5(2) K).

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.