Lattice Field Research Articles

Diffusion models as stochastic quantization in lattice field theory

In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. Using numerical simulations, we demonstrate that the DM can serve as a global sampler for generating quantum lattice field configurations in two-dimensional ϕ4 theory. We demonstrate that DMs can notably reduce autocorrelation times in the Markov chain, especially in the critical region where standard Markov Chain Monte-Carlo (MCMC) algorithms experience critical slowing down. The findings can potentially inspire further advancements in lattice field theory simulations, in particular in cases where it is expensive to generate large ensembles.

Localized Phonon Transport Study of GaN/SiO2 Core/shell Nanowires under Thermal-Stress Coupling.

In order to comprehensively explore the intricate mechanisms of thermo-mechanical interactions, this study employs the molecular dynamics method to investigate the influence of heat flux density, shell thickness and length, as well as stress on the radial interface phonon transport in GaN/SiO2 core/shell nanowire. Additionally, the surface eigenmode decomposition method is employed to analyze the interface phonon dispersion curves. The investigation reveals that with increasing heat flux density, internal thermal stresses intensify, leading to a complex distribution of thermal stresses within the system. Under the influence of thermal stress, the nonlinear acoustic properties interact with phonon scattering, resulting in the pronounced localization of interface phonons. Compressive stress causes an upshift in low-frequency phonons, while tensile stress induces a downward shift in the high-frequency optical branches at the interface. The localized phonon vibrations at the SiO2/GaN interface under nonuniform stress are identified as the primary cause for the abundant presence of nondispersive phonon modes at the radial interface. By elucidating the subtle interplay between lattice vibrations and stress fields, this study offers a novel and profound understanding of thermo-mechanical coupling effects, thereby providing innovative theoretical foundations for the design and performance management of thermoelectric devices.

Tensor renormalization group for fermions.

We review the basic ideas of the tensor renormalization group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. We discuss recent progress for entanglement filtering, loop optimization, bond-weighting techniques and matrix product decompositions for Grassmann tensor networks. The new methods are tested with two-dimensional Wilson-Majorana fermions and multi-flavor Gross-Neveu models. We show that the methods can also be applied to the fermionic Hubbard model in 1+1 and 2+1 dimensions.

Deformation localisation in ion-irradiated Fe and Fe10Cr

Determining the mechanisms for irradiation-induced ductility loss is crucial for the design of reactor structural components. Here, the deformation characteristics around nanoindents in Fe and Fe10Cr irradiated with Fe ions to ∼1 displacement-per-atom at 313 K are non-destructively studied. Slip steps surrounding the nanoindents indicate that deformation is localised in the irradiated materials. Lattice rotation and strain fields near the indent site show over 87% confinement of plasticity in the irradiated material. Cr has little effect on the irradiation-induced changes in pile-up topography and deformation fields, suggesting it has limited impact on retaining strain hardening capacity and reducing irradiation-induced embrittlement.

Feynman checkers: lattice quantum field theory with real time

Feynman checkers: lattice quantum field theory with real time

New basis for Hamiltonian SU(2) simulations

Due to rapidly improving quantum computing hardware, Hamiltonian simulations of relativistic lattice field theories have seen a resurgence of attention. This computational tool requires turning the formally infinite-dimensional Hilbert space of the full theory into a finite-dimensional one. For gauge theories, a widely used basis for the Hilbert space relies on the representations induced by the underlying gauge group, with a truncation that keeps only a set of the lowest dimensional representations. This works well at large bare gauge coupling, but becomes less efficient at small coupling, which is required for the continuum limit of the lattice theory. In this work, we develop a new basis suitable for the simulation of an SU(2) lattice gauge theory in the maximal tree gauge. In particular, we show how to perform a Hamiltonian truncation so that the eigenvalues of both the magnetic and electric gauge-fixed Hamiltonian are mostly preserved, which allows for this basis to be used at all values of the coupling. Little prior knowledge is assumed, so this may also be used as an introduction to the subject of Hamiltonian formulations of lattice gauge theories. Published by the American Physical Society 2024

Highly efficient mechanoluminescence of SrAl2–xYxO4:Eu2+,Dy3+ via trap regulation for dynamic signature anticounterfeiting

Mechanoluminescence (ML) materials have shown tremendous application potential due to their luminescent properties stimulated by mechanical energy. Owing to the narrow awareness of alterations in the crystal field environment of materials, the ML performance optimization is severely restricted. Here, a novel strategy of doping Y3+ into SrAl2O4:Eu2+,Dy3+ phosphors was employed by solid-phase reaction, significantly improving the ML performance. Based on analysis of structure and luminescent properties, it is proved that Y3+ occupies Al3+ sites, causing lattice expansion and crystal field distortion, altering trap engineering, strengthening carrier de-trapping ability, and improving ML performance. Through thermoluminescence (TL) analysis, the brighter ML behavior can be attributed to the carriers re-combination generated by high-density deep traps of 0.836 eV and above. Materials were also investigated in relation to pressure, stability and repeatability and conducive to achieving dynamic anticounterfeiting of personal signature. This study also provides more evidence that doping ions is an efficient tactic for greatly enhancing ML performance.

A deep-learning-based compact method for accelerating the electrowetting lattice Boltzmann simulations

Research on the electrowetting of micro- and nanoscale droplets is essential for microfluidics and nanomaterials applications. A lattice-Boltzmann-electrostatics (LBES) method is an effective and accurate method for simulating this process. However, the electric potential field in each time step requires numerous iterative calculations to converge. Therefore, there is a trade-off dilemma between using high-density lattice fields to improve simulation refinement and low-density lattice fields to reduce computing costs in simulations. Fortunately, deep learning techniques can enhance the computing efficiency of electric potential fields, providing an efficient and accurate solution for electrowetting studies in fine-grained fields. In this study, a compact LBES (C-LBES), a computationally accelerated model for an electric potential field with spatiotemporal prediction capability, is developed by combining the advantages of a recurrent residual convolutional unit and a convolutional long-short-term memory unit. A loss function incorporating a geometric boundary constraint term and a self-cyclic prediction scheme are introduced according to the characteristics of the prediction task, which further improves the prediction accuracy of the model and the computing efficiency of the electric potential field. The model is validated with small datasets, and the results show that the C-LBES model with the self-cyclic prediction scheme improves the computing efficiency of the conventional LBES method by a factor of 10 and provides high-precision results when predicting a two-dimensional convergent electric potential field with a lattice size of (110, 160). In the generalization experiments, the average absolute error of the calculated results remains in the same order of magnitude as the accuracy experimental results.

Can rooted staggered fermions describe nonzero baryon density at low temperatures?

Research on the quantum chromodynamics (QCD) phase diagram with lattice field theory methods is dominated by the use of rooted staggered fermions, as they are the computationally cheapest discretization available. We show that rooted staggered fermions at a nonzero baryochemical potential μB predict a sharp rise in the baryon density at low temperatures and μB≳3mπ/2, where mπ is the Goldstone pion mass. We elucidate the nature of the nonanalyticity behind this sharp rise in the density by a comparison of reweighting results with a Taylor expansion of high order. While at first sight this nonanalytic behavior becomes apparent at the same position where the pion condensation transition takes place in the phase-quenched theory, the nature of the nonanalyticity in the two theories appears to be quite different: While at nonzero isospin density the data are consistent with a genuine thermodynamic (branch-point) singularity, the results at nonzero baryon density point to an essential singularity at μB=0. The effect is absent for four flavors of degenerate quarks, where rooting is not used. For the two-flavor case, we show numerical evidence that the magnitude of the effect diminishes on finer lattices. We discuss the implications of this technical complication on future studies of the QCD phase diagram. Published by the American Physical Society 2024

Scalar field restricted Boltzmann machine as an ultraviolet regulator

Restricted Boltzmann machines (RBMs) are well-known tools used in machine learning to learn probability distribution functions from data. We analyze RBMs with scalar fields on the nodes from the perspective of lattice field theory. Starting with the simplest case of Gaussian fields, we show that the RBM acts as an ultraviolet regulator, with the cutoff determined by either the number of hidden nodes or a model mass parameter. We verify these ideas in the scalar field case, where the target distribution is known, and explore implications for cases where it is not known using the MNIST dataset. We also demonstrate that infrared modes are learnt quickest. Published by the American Physical Society 2024

Control variates for lattice field theory

In most lattice field theories, correlators are plagued by a signal-to-noise problem of exponential difficulty in the time separation. We propose a method for improving the signal-to-noise ratio, in which control variates are systematically constructed from lattice Schwinger-Dyson relations. The method is demonstrated on various two-dimensional lattices in scalar field theory, and a strategy for scaling to larger systems is explored. Published by the American Physical Society 2024

Correlation function distributions for O(N) lattice field theories in the disordered phase

Numerical computations in strongly interacting quantum field theories are often performed using Monte Carlo sampling methods. A key task in these calculations is to estimate the value of a given physical quantity from the distribution of stochastic samples that are generated using the Monte Carlo method. Typically, the sample mean and sample variance are used to define the expectation values and uncertainties of computed quantities. However, the Monte Carlo sample distribution contains more information than these basic properties, and it is useful to investigate it more generally. In this work, the exact form of the probability distributions of two-point correlation functions at zero momentum in O(N) lattice field theories in the disordered phase and in infinite volume are determined. These distributions allow for a robust investigation of the efficacy of the Monte Carlo sampling procedure and are shown also to allow for improved estimators of the target physical quantity to be constructed. The theoretical expectations are shown to agree with numerical calculations in the O(2) model. Published by the American Physical Society 2024

Remarks on discrete Dirac operators and their continuum limits

We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well known in the lattice field theory that the straightforward discretization of the Dirac operator introduces unwanted spectral subspaces, and it is known as the fermion doubling . In oder to overcome this difficulty, two methods were proposed. The first one is to introduce a new term, called the Wilson term , and the second one is the KS-fermion model or the staggered fermion model . We discuss mathematical formulations of these, and study their continuum limits.

Modeling of the femtosecond pulsed laser-induced damage of multi-layer dielectric gratings

The laser damage resistance of multi-layer dielectric gratings (MDGs) and metal multi-layer dielectric gratings (MMDGs) for femtosecond lasers directly determines the performance and life span of the high-energy laser system. It remains a significant challenge to predict the laser-induced damage threshold (LIDT) of MDGs and MMDGs for femtosecond lasers. Based on the nonlinear ionization and electric field intensity model, an effective method is proposed to calculate the LIDT of MDGs and MMDGs by introducing the dual temperature model. We take into account the evolutions of thermophysical parameters including the absorption coefficient, heat capacity, and thermal conductivity of the dielectric material as a function of the free-electron density and temperature. The free electron density of the conduction band combined with the electric field strength inside the grating can be calculated by the laser-induced ionization theory, more importantly, the transient distribution of the lattice temperature field generated by femtosecond laser irradiated grating excitation is obtained by the two-temperature model (TTM). This work is beneficial for guiding the design and fabrication of MDGs and MMDGs with high-LIDTs for ultra-short ultra-intense laser systems.

Improved information criteria for Bayesian model averaging in lattice field theory

Improved information criteria for Bayesian model averaging in lattice field theory

Semi-Coherent Heterointerface Engineering via In Situ Phase Transition for Enhanced Sodium/Lithium-Ions Storage.

To improve ion transport kinetics and electronic conductivity between the different phases in sodium/lithium-ion battery (LIB/SIB) anodes, heterointerface engineering is considered as a promising strategy due to the strong built-in electric field. However, the lattice mismatch and defects in the interphase structure can lead to large grain boundary resistance, reducing the ion transport kinetics and electronic conductivity. Herein, monometallic selenide Fe3Se4-Fe7Se8 semi-coherent heterointerface embedded in 3D connected Nitrogen-doped carbon yolk-shell matrix (Fe3Se4-Fe7Se8@NC) is obtained via an in situ phase transition process. Such semi-coherent heterointerface between Fe3Se4 and Fe7Se8 shows the matched interfacial lattice and strong built-in electric field, resulting in the low interface impedance and fast reaction kinetics. Moreover, the yolk-shell structure is designed to confine all monometallic selenide Fe3Se4-Fe7Se8 semi-coherent heterointerface nanoparticles, improving the structural stability and inhibiting the volume expansion effect. In particular, the 3D carbon bridge between multi-yolks shell structure improves the electronic conductivity and shortens the ion transport path. Therefore, the efficient reversible pseudocapacitance and electrochemical conversion reaction are enabled by the Fe3Se4-Fe7Se8@NC, leading to the high specific capacity of 439mAhg-1 for SIB and 1010mAhg-1 for LIB. This work provides a new strategy for constructing heterointerface of the anode for secondary batteries.

Floquet insulators and lattice fermions beyond naive time discretization

Periodically driven quantum systems known as Floquet insulators can host topologically protected bound states known as “π modes” that exhibit response at half the frequency of the drive. Such states can also appear in undriven lattice field theories when time is discretized as a result of fermion doubling, raising the question of whether these two phenomena could be connected. Recently we demonstrated such a connection at the level of an explicit mapping between the spectra of a continuous-time Floquet model and a discrete-time undriven lattice fermion model. However, this mapping relied on a symmetry of the single-particle spectrum that is not present for generic drive parameters. Inspired by the example of the temporal Wilson term in lattice field theory, in this paper we extend this mapping to the full drive parameter space by allowing the parameters of the discrete-time model to be frequency-dependent. The spectra of the resulting lattice fermion models exactly match the quasienergy spectrum of the Floquet model in the thermodynamic limit. Our results demonstrate that spectral features characteristic of beyond-equilibrium physics in Floquet systems can be replicated in static systems with appropriate time discretization. Published by the American Physical Society 2024

Equivalence of lattice operators and graph matrices

Abstract We explore the relationship between lattice field theory and graph theory, placing special emphasis on the interplay between Dirac and scalar lattice operators and matrices within the realm of spectral graph theory. Beyond delving into fundamental concepts of spectral graph theory, such as adjacency and Laplacian matrices, we introduce a novel matrix called an “antisymmetrized adjacency matrix”, specifically tailored for cycle digraphs (T1 lattice) and simple directed paths (B1 lattice). The nontrivial relationship between graph theory matrices and lattice operators shows that the graph Laplacian matrix mirrors the lattice scalar operator and the Wilson term in lattice fermions, while the antisymmetrized adjacency matrix, along with its extensions to higher dimensions, is equivalent to naive lattice Dirac operators. Building upon these connections, we provide rigorous proofs for two key assertions: (i) The count of zero-modes in a free lattice scalar operator coincides with the zeroth Betti number of the underlying graph (lattice). (ii) The maximum count of Dirac zero-modes in a free lattice fermion operator is equivalent to the cumulative sum of all Betti numbers when the D-dimensional graph results from a Cartesian product of cycle digraphs (T1 lattice) and simple directed paths (B1 lattice).

Training normalizing flows with computationally intensive target probability distributions

Machine learning techniques, in particular the so-called normalizing flows, are becoming increasingly popular in the context of Monte Carlo simulations as they can effectively approximate target probability distributions. In the case of lattice field theories (LFT) the target distribution is given by the exponential of the action. The common loss function's gradient estimator based on the “reparametrization trick” requires the calculation of the derivative of the action with respect to the fields. This can present a significant computational cost for complicated, non-local actions like e.g. fermionic action in QCD. In this contribution, we propose an estimator for normalizing flows based on the REINFORCE algorithm that avoids this issue. We apply it to two dimensional Schwinger model with Wilson fermions at criticality and show that it is up to ten times faster in terms of the wall-clock time as well as requiring up to 30% less memory than the reparameterization trick estimator. It is also more numerically stable allowing for single precision calculations and the use of half-float tensor cores. We present an in-depth analysis of the origins of those improvements. We believe that these benefits will appear also outside the realm of the LFT, in each case where the target probability distribution is computationally intensive.

Regulating the lattice strain field by high-entropy strategy to realize the conformal growth of perovskites for efficient oxygen evolution

Perovskite oxides show great promise in the field of water electrolysis due to their low cost and tailorable properties. However, their performance is seriously constrained by crystal agglomeration. Herein, a high-entropy strategy is reported to regulate the lattice strain field, endowing the crystal with a high energy barrier and optimizing its surface properties to achieve conformal growth of highly reactive perovskite oxides. A range of characterization methods and theoretical calculations are used to investigate the lattice distortion-induced complex lattice strain field and the effective activation strategy of the cocktail effect. Based on this, the produced rod-like La(CoFeNiCrAl)O3 (La5B–Al) exhibits a low overpotential of 285 mV at 10 mA cm−2 in 1 M KOH. This work provides a novel strategy to use the lattice strain field for regulating the growth of catalysts and clarifies the relationship between high-entropy effects and material properties.