Search NASA⌕ Search

SEARCH · Search NASA

Results for “Symmetry functions”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Scalar modular bootstrap and zeros of the Riemann zeta function

Using the technology of harmonic analysis, we derive a crossing equation that acts only on the scalar primary operators of any two-dimensional conformal field theory with U(1) c symmetry. From this crossing equation, we derive bounds on the scalar gap of all such theories. Rather remarkably, our crossing equation contains information about all nontrivial zeros of the Riemann zeta function. As a result, we rephrase the Riemann hypothesis purely as a statement about the asymptotic density of scalar operators in certain two-dimensional conformal field theories. We discuss generalizations to theories with only Virasoro symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Near conformal perturbation theory in SYK type models

We present a systematic procedure to extract the dynamics of the low energy soft mode in SYK type models with a single energy scale J and emergent reparametrization symmetry in the IR. This is given in the framework of the perturbative scheme of arXiv:1608.07567 based on a specific (off-shell) breaking of conformal invariance in the UV, adjusted to yield the exact large-N saddle point. While this breaking term formally vanishes on-shell, it has a non-trivial effect on correlation functions and the effective action. In particular, it leads to the Schwarzian action with a specific coupling to bi-local matter. The method is applied to the evaluation of O(1) corrections to the correlation function of bi-locals. As a byproduct we confirm precise agreement with the explicit, symmetry breaking procedure. We provide a verification in the large q limit (Liouville theory), where the correlators can be calculated exactly at all length scales. In this case, our scheme illuminates how the enhanced O(J) and the subleading O(1) contributions originate from the Schwarzian dynamics of the soft mode and its interaction with h = 2 (bi-local) matter.

1/N expansion↗
DOE OSTI2022

Probing of Local Structure in Laves Compound TbFe 2

Abstract The Laves compounds Tb 1‐x Dy x Fe 2 have attracted much interest due to the giant magnetostriction effect appearing at their morphotropic phase boundary compositions. Although previous studies have established the relationship between the average structure and magnetostrictive properties in these compounds, there is a lack of characterization of their local structures. In this paper, as a first step toward this goal, the evolution of the local structure of the terminal compound (TbFe 2 ) of this system is reported, in an attempt to provide useful information about interatomic bonding in this system. The pair distribution function (PDF) results suggest that the compound presents the rhombohedral local crystal symmetry. The lattice at the local scale shows abnormal thermal expansion which is different from the long scale structure. The different role of the Tb─Fe bond and Fe─Fe bond in affecting the crystal lattice is revealed. These findings highlight the important role of local structure in determining the magnetostrictive properties of the Laves compounds.

Kou, Ronghui↗
DOE OSTI2020

Rapid generation of optimal generalized Monkhorst-Pack grids

In this report computational modeling of the properties of crystalline materials has become an increasingly important aspect of materials research, consuming hundreds of millions of CPU-hours at scientific computing centers around the world each year, if not more. A routine operation in such calculations is the evaluation of integrals over the Brillouin zone. We have previously demonstrated that performing such integrals using generalized Monkhorst-Pack k-point grids can roughly double the speed of these calculations relative to the widely-used traditional Monkhorst-Pack grids. However the generation of optimal generalized Monkhorst-Pack grids is not implemented in most software packages due to the computational cost and difficulty of identifying the best grids. To address this problem, we present new algorithms that allow rapid generation of optimal generalized Monkhorst-Pack grids on the fly. We demonstrate that the grids generated by these algorithms are on average significantly more efficient than those generated using existing algorithms across a range of grid densities. For grids that correspond to a real-space supercell with at least 50 Å between lattice points, which is sufficient to converge density functional theory calculations within 1 meV/atom for nearly all materials, our algorithm finds optimized grids in an average of 0.19 s on a single processing core. To facilitate the widespread adoption of this approach, we present new open-source tools including a library designed for integration with third-party software packages.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Investigating phase transitions from local crystallographic analysis based on statistical learning of atomic environments in 2D MoS 2 -ReS 2

Traditionally, phase transitions are explored using a combination of macroscopic functional characterization and scattering techniques, providing insight into the average properties and symmetries of the lattice but local atomic level mechanisms during phase transitions generally remain unknown. Here, we explore the mechanisms of a phase transition between the trigonal prismatic and distorted octahedral phases of layered chalcogenides in the 2D MoS 2 - ReS 2 system from the observations of local degrees of freedom, namely atomic positions by Scanning Transmission Electron Microscopy (STEM). We employ local crystallographic analysis based on statistical learning of atomic environments to build a picture of the transition from the atomic level up and determine local and global variables controlling the local symmetry breaking. In particular, we argue that the dependence of the average symmetry breaking distortion amplitude on global and local concentration can be used to separate local chemical as well as global electronic effects on transition. This approach allows exploring atomic mechanisms beyond the traditional macroscopic descriptions, utilizing the imaging of compositional fluctuations in solids to explore phase transitions over a range of realized and observed local stoichiometries and atomic configurations.

25 ENERGY STORAGE↗
DOE OSTI2025

Dissipative Phase Transition in the Two-Photon Dicke Model

We explore the dissipative phase transition of the two-photon Dicke model, a topic that has garnered significant attention recently. Our analysis reveals that while single-photon loss does not stabilize the intrinsic instability in the model, the inclusion of two-photon loss restores stability, leading to the emergence of superradiant states, which coexist with the normal vacuum states. Using a second-order cumulant expansion for the photons, we derive an analytical description of the system in the thermodynamic limit, which agrees well with the exact calculation results. Additionally, we present the Wigner function for the system, shedding light on the breaking of the 𝑍4 symmetry inherent in the model. These findings offer valuable insights into stabilization mechanisms in open quantum systems and pave the way for exploring complex nonlinear dynamics in two-photon Dicke models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Variational study of the Kitaev-Heisenberg-Gamma model

Here we compute the low-energy excitation spectrum and the dynamical spin structure factor of the Kitaev-Heisenberg-Gamma model through a variational approach based on the exact fractionalized excitations of the pure Kitaev honeycomb model. This novel approach reveals the physical reason for the asymmetric stability of the Kitaev spin liquid phases around the ferromagnetic and antiferromagnetic Kitaev limits. Moreover, we demonstrate that the fractionalized excitations form bound states in specific regions of each Kitaev spin liquid phase and that certain phase transitions induced by Heisenberg and Gamma interactions are driven by the condensation of such a bound state. Remarkably, this bound state appears as a sharp mode in the dynamical spin structure factor, while its condensation patterns at the appropriate phase transitions provide a simple explanation for the magnetically ordered phases surrounding each Kitaev spin liquid phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Planar Hall Driven Torque in a Ferromagnet/Nonmagnet/Ferromagnet System

An important goal of spintronics is to covert a charge current into a spin current with a controlled spin polarization that can exert torques on an adjacent magnetic layer. Here we demonstrate such torques in a two ferromagnet system. A CoNi multilayer is used as a spin current source in a sample with structure CoNi/Au/CoFeB. Spin torque ferromagnetic resonance is used to measure the torque on the CoFeB layer. The response as a function of the applied field angle and current is consistent with the symmetry expected for a torque produced by the planar Hall effect originating in CoNi. We find the strength of this effect to be comparable to that of the spin Hall effect in platinum, indicating that the planar Hall effect holds potential as a spin current source with a controllable polarization direction.

ferromagnetic resonance↗
DOE OSTI2023

Nuclear-Level Effective Theory of 𝜇 → 𝑒 Conversion

The Mu2e and COMET 𝜇 → 𝑒 conversion experiments are expected to significantly advance limits on new sources of charged lepton flavor violation. Almost all theoretical work in the field has focused on just two operators. However, general symmetry arguments lead to a 𝜇 → 𝑒 conversion rate with six response functions, each of which, in principle, is observable by varying nuclear properties of targets. We construct a nucleon-level nonrelativistic effective theory (NRET) to clarify the microscopic origin of these response functions and to relate rate measurements in different targets. This exercise identifies three operators and their small parameters that control the NRET operator expansion. We note inconsistencies in past treatments of these parameters. The NRET is technically challenging, involving 16 operators, several distorted electron partial waves, bound muon upper and lower components, and an exclusive nuclear matrix element. We introduce a trick for treating the electron Coulomb effects accurately, which enables us to include all of these effects while producing transition densities whose one-body matrix elements can be evaluated analytically, greatly simplifying the nuclear physics. We derive bounds on operator coefficients from existing and anticipated 𝜇 → 𝑒 conversion experiments. We discuss how similar NRET formulations have impacted dark matter phenomenology, noting that the tools this community has developed could be adapted for charged lepton flavor violation studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Short-range order parameter expansions for simple configurational energetics

Local chemical environments of multicomponent crystals are parametrized according to basis vectors of their irreducible invariant subspaces. These short-range order parameters enable Taylor expansions of configurational properties that easily incorporate additional couplings. As one example, expansions including long-range composition can describe the energies of many alloys more accurately than conventional cluster expansions while using far fewer neighbors and basis functions.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Investigating the electrical transport properties and electronic structure of Zr 2 ⁢CuSb 3

The checkerboard lattice has been proposed to host topological flat bands as a result of destructive interference among its various electronic hopping terms. However, it has proven challenging to realize experimentally due to the difficulty of isolating this structure from any significant out-of-plane bonding while maintaining structural integrity. Here, in this study, single crystals of Zr 2 CuSb 3 , a potential candidate for the checkerboard lattice, were synthesized using the solution (self-flux) method, and their structure was confirmed via x-ray diffraction. Electrical-transport measurements indicate metallic behavior with electron-dominated carriers. Angle-resolved photoemission spectroscopy reveals multiple electron pockets and significant k z broadening due to its large c axis and low dispersion features in k z . Density-functional theory (DFT) calculations further disentangle the contributions from each high-symmetry plane, providing a comprehensive characterization of electronic behavior. The DFT calculations were then used to determine the orbital contributions of the bands and detect the out-of-plane bonding which prevented the flat bands from forming.

Downey, Eoghan [Univ. of Michigan, Ann Arbor, MI (↗
NASA NTRS1981

Deep anistropic shell program for tire analysis

A finite element program was constructed to model the mechanical response of a tire, treated as a deep anisotropic shell, to specified static loads. The program is based on a Sanders Budiansky type shell theory with the effects of transverse shear deformation and bending-extensional coupling included. A displacement formulation is used together with a total Lagrangian description of the deformation. Sixteen-node quadrilateral elements with bicubic shape functions are employed. The Noor basis reduction technique and various type of symmetry considerations serve to improve the computational efficiency.

Andersen, C. M.↗
DOE OSTI2025

Chemical Control of Symmetry and Bandgap in Tungsten Oxyhalide van der Waals Semiconductors

Tunability in solid-state materials is essential for testing theory, discovering quantum phases, and enabling functionality. Layered van der Waals (vdW) semiconductors offer a unique platform, providing new degrees of freedom at the two-dimensional (2D) limit through exfoliation and external controls. Here, in this study, we demonstrate tunability of symmetry and electronic structure via halogen substitution in a family of layered vdW tungsten oxyhalides. Substituting the halogens in WO 2 X 2 (X = I, Br, Cl) tunes the bandgap across a broad energy range and modifies the structural symmetry from centrosymmetric to noncentrosymmetric. By alloying WO 2 I 2– y Br y , we continuously tune the polar distortion and optical gap across the visible range. These insights into halogen substitution effects on symmetry and electronic structure lay the foundation for new tunable vdW semiconductors for optoelectronics and nonlinear optics.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Variational quantum simulation of the critical Ising model with symmetry averaging

Here we investigate the use of deep multiscale entanglement renormalization ansatz (DMERA) circuits as a variational ansatz. We use the exactly solvable one-dimensional critical transverse-field Ising model as a test bed. Numerically exact simulation of the quantum circuit ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, the DMERA strongly outperforms a standard quantum approximate optimization algorithm (QAOA)–style ansatz, and that a major source of systematic error in correlation functions approximated using the DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. Here, we propose that this technique for mitigating systematic error could be applied to noisy intermediate-scale quantum (NISQ) simulations of physical systems with other symmetries.

1-dimensional spin chains↗
DOE OSTI2024

Scale and conformal invariance on (A)dS spacetimes

We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general two-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension D > 4 , these conformal theories can be diagonalized into standard massive fields in which unbroken conformal symmetry nontrivially mixes components of different spins. In D = 4 , the tensor case becomes a conformal theory mixing a partially massless spin-2 field with a massless spin-1 field. For massless linearized gravity in D = 4 , we confirm through direct calculation that correlation functions of gauge-invariant operators take the conformally invariant form, despite the absence of standard conformal symmetry at the level of the action. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2026

Soft symmetries of topological orders

(2+1)D topological orders possess emergent symmetries given by a group $\text{Aut}(\mathcal{C})$, which consists of the braided tensor autoequivalences of the modular tensor category $\mathcal{C}$ that describes the anyons. In this paper we discuss cases where $\text{Aut}(\mathcal{C})$ has elements that neither permute anyons nor are associated to any symmetry fractionalization but are still non-trivial, which we refer to as soft symmetries. We point out that one can construct topological defects corresponding to such exotic symmetry actions by decorating with a certain class of gauged SPT states that cannot be distinguished by their torus partition function. This gives a physical interpretation to work by Davydov on soft braided tensor autoequivalences. This has a number of important implications for the classification of gapped boundaries, non-invertible spontaneous symmetry breaking, and the general classification of symmetry-enriched topological phases of matter. Here, we also demonstrate analogous phenomena in higher dimensions, such as (3+1)D gauge theory with gauge group given by the quaternion group $Q_8$.

Gauge theory techniques↗
DOE OSTI2023

Symmetries and spectral statistics in chaotic conformal field theories

We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large central charge. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic properties of the spectrum from those which are a consequence of Virasoro symmetry and modular invariance. We argue that random matrix universality in the near-extremal limit is an independent feature of each spin sector separately; this is a non-trivial statement because the exact spectrum is fully determined by only the spectrum of spin zero primaries and those of a single non-zero spin (“spectral determinacy”). We then describe an argument analogous to the one leading to Cardy’s formula for the averaged density of states, but in our case applying it to spectral correlations: assuming statistical universalities in the near-extremal spectrum in all spin sectors, we find similar random matrix universality in a large spin regime far from extremality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗