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DOE OSTI2022

Report of the Snowmass 2021 Topical Group on Lattice Gauge Theory

Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Status of Lattice QCD Calculations of One and Two-Nucleon Matrix Elements

Lattice QCD calculations of basic hadronic quantities are now often performed with systematic control over the physical pion mass, continuum and infinite volume limits. This progress signals a new era in which lattice QCD will be used to compute basic properties of hadrons, nucleons and light nuclei directly from the Standard Model (SM). In particular, we will be able to use lattice QCD, combined with Effective Field Theory, to make quantitative statements about the interaction of SM matter and potential beyond the SM physics ranging from direct dark matter detection to permanent electric dipole moments. I will briefly review the status and challenges of lattice QCD calculations of select one- and two-nucleon matrix elements. These calculations are significantly more challenging than the basic quantities computed with all systematics controlled, but substantial progress is being made.

Walker-Loud, Andre↗

DOE OSTI2023

Structural metamaterials comprising interpenetrating lattices

Multi-body interpenetrating lattices comprise two or more lattices that interlace or interpenetrate through the same volume without any direct physical connection to each other, wherein energy transfer is controlled by surface interactions. As a result, multifunctional or composite-like responses can be achieved by additive manufacturing of the interpenetrating lattices, even with only a single print material, with programmable interface-dominated properties. As a result, the interpenetrating lattices can have unique mechanical properties, including improved toughness, multi-stable/negative stiffness, and electromechanical coupling.

Boyce, Brad↗

DOE OSTI2026

$B \to π$, $B_{(s)} \to D_{(s)}$ from 2+1+1 Flavor Lattice QCD

We present a lattice-QCD calculation of the hadronic form factors for $B$-meson semileptonic decays computed using the highly improved staggered quark action for both valence and sea quarks on the MILC collaborations 2+1+1-flavor ensembles with lattice spacing ranging from 0.09 fm to 0.03 fm, many with physical pion masses On our finest ensembles, we compute the form factors directly at the physical $b$-quark mass. We discuss the computational setup and analysis strategies for two- and three-point correlation functions. For $B_{(s)} \to D_{(s)}$ we present preliminary results of chiral-continuum fits for the scalar and vector form factors. The goal of this project is a percent-level determination of the scalar and vector form factors to enable high-precision determinations of $|V_{ub}|$ and $|V_{cb}|$. This work fits into a broader program of lattice-QCD studies of weak $B$-meson decays by the Fermilab Lattice and MILC Collaborations.

Cassar, Nicholas [Colorado State U.]↗

DOE OSTI2021

Nucleon momentum fraction, helicity and transversity from 2+1-flavor lattice QCD

A detailed analysis of the systematic uncertainties in the calculation of the isovector momentum fraction, ( x ) u - d , helicity moment, ( x ) Δ u - Δ d , and the transversity moment, ( x ) δu - δd , of the nucleon is presented using high-statistics data on seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using 2 + 1-flavors of dynamical Wilson-clover quarks. The much higher statistics have facilitated better control over all systematics compared to previous lattice calculations. The least understood systematic — excited-state contamination — is quantified by studying the variation of the results as a function of different estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions, and as a function of the pion mass M π . The final results are obtained using a simultaneous fit in the lattice spacing a , pion mass M π and the finite volume parameter M π L keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. Our final results, in the $ \overline{\mathrm{MS}} $ scheme at 2 GeV, are ( x ) u - d = 0 . 155(17)(20), ( x ) Δ u - Δ d = 0 . 183(14)(20) and ( x ) δu - δd = 0 . 220(18)(20), where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with phenomenological global fit values.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

In-medium bottomonium properties from lattice NRQCD calculations with extended meson operators

We calculate the temperature dependence of bottomonium correlators in (2+1)-flavor lattice QCD with the aim to constrain in-medium properties of bottomonia at high temperature. The lattice calculations are performed using HISQ action with physical strange quark mass and light quark masses twenty times smaller than the strange quark mass at two lattice spacings a = 0.0493 fm and 0.0602 fm, and temporal extents N τ = 16 − 30, corresponding to the temperatures T = 133 − 250 MeV. We use a tadpole-improved NRQCD action including spin-dependent v 6 corrections for the heavy quarks and extended meson operators in order to be sensitive to in-medium properties of the bottomonium states of interest. We find that within estimated errors the bottomonium masses do not change compared to their vacuum values for all temperatures under our consideration; however, we find different nonzero widths for the various bottomonium states.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

The continuum and leading twist limits of parton distribution functions in lattice QCD

In this study, we present continuum limit results for the unpolarized parton distribution function of the nucleon computed in lattice QCD. This study is the first continuum limit using the pseudo-PDF approach with Short Distance Factorization for factorizing lattice QCD calculable matrix elements. Our findings are also compared with the pertinent phenomenological determinations. Inter alia, we are employing the summation Generalized Eigenvalue Problem (sGEVP) technique in order to optimize our control over the excited state contamination which can be one of the most serious systematic errors in this type of calculations. A crucial novel ingredient of our analysis is the parameterization of systematic errors using Jacobi polynomials to characterize and remove both lattice spacing and higher twist contaminations, as well as the leading twist distribution. This method can be expanded in further studies to remove all other systematic errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Constraints on charm-anticharm asymmetry in the nucleon from lattice QCD

We present the first lattice QCD calculation of the charm quark contribution to the nucleon electromagnetic form factors $G^c_{E,M}(Q^2)$ in the momentum transfer range $0\leq Q^2 \leq 1.4$ $\rm GeV^2$. The quark mass dependence, finite lattice spacing and volume corrections are taken into account simultaneously based on the calculation on three gauge ensembles including one at the physical pion mass. The nonzero value of the charm magnetic moment $\mu^c_M=-0.00127(38)_{\rm stat}(5)_{\rm sys}$, as well as the Pauli form factor, reflects a nontrivial role of the charm sea in the nucleon spin structure. The nonzero $G^c_{E}(Q^2)$ indicates the existence of a nonvanishing asymmetric charm-anticharm sea in the nucleon. Performing a nonperturbative analysis based on holographic QCD and the generalized Veneziano model, we study the constraints on the $[c(x)-\bar{c}(x)]$ distribution from the lattice QCD results presented here. Our results provide complementary information and motivation for more detailed studies of physical observables that are sensitive to intrinsic charm and for future global analyses of parton distributions including asymmetric charm-anticharm distribution.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Magnetic ground states of honeycomb lattice Wigner crystals

Lattice Wigner crystal states stabilized by long-range Coulomb interactions have recently been realized in two-dimensional moiré materials. We employ large-scale unrestricted Hartree-Fock techniques to unveil the magnetic phase diagrams of honeycomb lattice Wigner crystals. For the three lattice filling factors with the largest charge gaps, $n=2/3,1/2,1/3$, the magnetic phase diagrams contain multiple phases, including ones with non-collinear and non-coplanar spin arrangements. We discuss magnetization evolution with external magnetic field, which has potential as an experimental signature of exotic spin states. Our theoretical results could potentially be validated in moiré materials formed from group VI transition metal dichalcogenide twisted homobilayers.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Beyond single crystals: Imaging rubrene polymorphism across crystalline batches through lattice phonon Raman microscopy

Polymorphism is an issue troubling numerous scientific fields. A phenomenon where molecules can arrange in different orientations in a crystal lattice, polymorphism in the field of organic photovoltaic materials can dramatically change electronic properties of these materials. Rubrene is a benchmark photovoltaic material showing high carrier mobility in only one of its three polymorphs. To use rubrene in devices, it is important to quantify the polymorph distribution arising from a particular crystal growth method. However, current methods for characterizing polymorphism are either destructive or inefficient for batch scale characterization. Lattice phonon Raman spectroscopy has the ability to distinguish between polymorphs based on low frequency intermolecular vibrations. Here, we present here the addition of microscopy to lattice phonon Raman spectroscopy, which allows us to not only characterize polymorphs efficiently and nondestructively through Raman spectroscopy but also concurrently gain information on the size and morphology of the polymorphs. We provide examples for how this technique can be used to perform large, batch scale polymorph characterization for crystals grown from solution and physical vapor transport.We end with a case study showing how Raman microscopy can be used to efficiently optimize a green crystal growth method, selecting for large orthorhombic crystals desired for rubrene electronic device applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Anharmonic lattice dynamics and superionic transition in AgCrSe 2

Intrinsically low lattice thermal conductivity ( κ l a t ) in superionic conductors is of great interest for energy conversion applications in thermoelectrics. Yet, the complex atomic dynamics leading to superionicity and ultralow thermal conductivity remain poorly understood. Here, we report a comprehensive study of the lattice dynamics and superionic diffusion in A g C r S e 2 from energy- and momentum-resolved neutron and X-ray scattering techniques, combined with first-principles calculations. Our results settle unresolved questions about the lattice dynamics and thermal conduction mechanism in A g C r S e 2 . We find that the heat-carrying long-wavelength transverse acoustic (TA) phonons coexist with the ultrafast diffusion of Ag ions in the superionic phase, while the short-wavelength nondispersive TA phonons break down. Strong scattering of phonon quasiparticles by anharmonicity and Ag disorder are the origin of intrinsically low κ l a t . The breakdown of short-wavelength TA phonons is directly related to the Ag diffusion, with the vibrational spectral weight associated to Ag oscillations evolving into stochastic decaying fluctuations. Furthermore, the origin of fast ionic diffusion is shown to arise from extended flat basins in the energy landscape and collective hopping behavior facilitated by strong repulsion between Ag ions. These results provide fundamental insights into the complex atomic dynamics of superionic conductors.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Spin-lattice model for cubic crystals

In this work, we present a methodology based on the Néel model to build a classical spin-lattice Hamiltonian for cubic crystals capable of describing magnetic properties induced by the spin-orbit coupling like magnetocrystalline anisotropy and anisotropic magnetostriction, as well as exchange magnetostriction. Taking advantage of the analytical solutions of the Néel model, we derive theoretical expressions for the parametrization of the exchange integrals and Néel dipole and quadrupole terms that link them to the magnetic properties of the material. This approach allows us to build accurate spin-lattice models with the desired magnetoelastic properties. We also explore a possible way to model the volume dependence of magnetic moment based on the Landau energy. This feature allows us to consider the effects of hydrostatic pressure on the saturation magnetization. We apply this method to develop a spin-lattice model for BCC Fe and FCC Ni, and we show that it accurately reproduces the experimental elastic tensor, magnetocrystalline anisotropy under pressure, anisotropic magnetostrictive coefficients, volume magnetostriction, and saturation magnetization under pressure at zero temperature. This work could constitute a step towards large-scale modeling of magnetoelastic phenomena.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Low-energy limit of some exotic lattice theories and UV/IR mixing

We continue our exploration of exotic, gapless lattice and continuum field theories with subsystem global symmetries. In an earlier paper, we presented free lattice models enjoying all the global symmetries (except continuous translations), dualities, and anomalies of the continuum theories. Here, we study in detail the relation between the lattice models and the corresponding continuum theories. We do that by analyzing the spectrum of the theories and several correlation functions. These lead us to uncover interesting subtleties in the way the continuum limit can be taken. In particular, in some cases, the infinite volume limit and the continuum limit do not commute. Furthermore, this signals a surprising UV/IR mixing, i.e., long distance sensitivity to short distance details.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Unconventional skyrmions in an interfacial frustrated triangular lattice

Magnetic skyrmions are spin topological textures of potential interest in spintronics-related data storage and processing devices. Here, in this work, we show the emergence of unconventional skyrmions in a geometrically frustrated triangular lattice on an inversion-symmetry-breaking two-dimensional electron gas substrate. Starting with a classical double-exchange mechanism, this generic interface induces exotic skyrmionic and unique noncoplanar magnetic states not observed in the equivalent square lattice interface. We study the model by deriving an effective spin Hamiltonian. Large scale classical Monte Carlo simulations provide a quantitative evidence for the emergence of these exotic magnetic states. We found that these chiral magnetic states exhibit a substantial and nonzero topological Hall conductivity. As potential material candidates, we propose Cr/MoS 2 , Fe/MoS 2 , and Fe/WSe 2 interfaces because they have the requisite underlying triangular lattice structures and large spin-orbit coupling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Lattice Effective Field Theory Simulations of Nuclei

Lattice effective field theory applies the principles of effective field theory in a lattice framework where space and time are discretized. Nucleons are placed on the lattice sites, and the interactions are tuned to replicate the observed features of the nuclear force. Monte Carlo simulations are then employed to predict the properties of nuclear few- and many-body systems. Here, we review the basic methods and several theoretical and algorithmic advances that have been used to further our understanding of atomic nuclei.

nuclear lattice effective field theory↗

NASA NTRS1996

Effects of Lattice Distortion and Jahn-Teller Coupling on the Magnetoresistance of La(sub 0.7)Ca(sub 0.3)MnO(sub 3) and La(sub 0.5)Ca(sub 0.5)CoO(sub 3) Epitaxial Films

Studies of La(sub 0.7)Ca(sub 0.3)MnO(sub 3) epitaxial films on substrates with a range of lattice constants reveal two dominant contributions to the occurence of colossal negative magnetoresistance (CMR) in these manganites:...We therefore suggest that lattice polaron conduction associated with Jahn-Teller coupling is essential for the occurence of CMR, and that lattice distortion further enhances the CMR effect in the manganites.

lattice distortion epitaxial films lattice polaron↗

DOE OSTI2024

Transverse Momentum Distributions from Lattice QCD without Wilson Lines

The transverse-momentum-dependent distributions (TMDs), which are defined by gauge-invariant 3D parton correlators with staple-shaped lightlike Wilson lines, can be calculated from quark and gluon correlators fixed in the Coulomb gauge on a Euclidean lattice. These quantities can be expressed gauge invariantly as the correlators of Coulomb-gauge-dressed fields, which reduce to the standard TMD correlators under principal-value prescription in the infinite boost limit. In the framework of large-momentum effective theory, a quasi-TMD defined from such correlators in a large-momentum hadron state can be matched to the TMD via a factorization formula, whose exact form is derived using soft collinear effective theory and verified at one-loop order. Compared to the currently used gauge-invariant correlators, this new method can substantially improve statistical precision and simplify renormalization for the time-reversal-even TMDs, which will greatly enhance the predicative power of lattice QCD in the nonperturbative region.

Effective field theory↗

DOE OSTI2023

Direct Observation of Magnetic Bubble Lattices and Magnetoelastic Effects in van der Waals Cr 2 Ge 2 Te 6

Abstract Ferromagnetic van der Waals (vdW) materials are of large current interest for the fundamental study of low‐dimensional magnetism and for potential applications in multilayer heterostructures. Cr 2 Ge 2 Te 6 (CGT) is particularly exciting because it is a ferromagnetic semiconductor with tunable electronic and magnetic properties. Controlling the magnetic domain structure of CGT is a requirement for understanding its novel interface physics and for tuning behavior for potential devices. Herein, cryo‐Lorentz transmission electron microscopy is performed in the temperature range of 12–50K to directly image the magnetic domain structures in CGT. A rich phase diagram of domain structures including stripe domains, magnetic bubble lattices of mixed‐chirality, and topologically‐protected lattices of homochiral magnetic bubbles is observed. The types and chiralities of the bubbles can be controlled by topographical changes in the CGT flakes. Additionally, it is observed that in‐plane strain and magnetoelastic coupling can align and organize both bubble lattices and stripe domains. This study provides insights into creating and controlling complex magnetic domain structures for integration into multilayer heterostructures and for future studies of 2D magnetism.

36 MATERIALS SCIENCE↗