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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Twisted bilayer graphene. I. Matrix elements, approximations, perturbation theory, and a k · p two-band model

We investigate the twisted bilayer graphene (TBG) model of Bistritzer and MacDonald (BM) [Bistritzer and MacDonald, Proc. Natl. Acad. Sci. 108, 12233 (2011)] to obtain an analytic understanding of its energetics and wave functions needed for many-body calculations. We provide an approximation scheme for the wave functions of the BM model, which first elucidates why the BM K M -point centered original calculation containing only four plane waves provides a good analytical value for the first magic angle (θ M ≈ 1°). The approximation scheme also elucidates why most of the many-body matrix elements in the Coulomb Hamiltonian projected to the active bands can be neglected. By applying our approximation scheme at the first magic angle to a Γ M -point centered model of six plane waves, we analytically understand the reason for the small Γ M -point gap between the active and passive bands in the isotropic limit w 0 = w 1 . Furthermore, we analytically calculate the group velocities of the passive bands in the isotropic limit, and show that they are almost doubly degenerate, even away from the Γ M point, where no symmetry forces them to be. Furthermore, moving away from the Γ M and K M points, we provide an explicit analytical perturbative understanding as to why the TBG bands are flat at the first magic angle, despite the first magic angle is defined by only requiring a vanishing K M -point Dirac velocity. We derive analytically a connected “magic manifold” w 1 = $2\sqrt{1 + w^{2}_{0}}$ $-\sqrt{2 + 3w^2_0}$, on which the bands remain extremely flat as w 0 is tuned between the isotropic (w 0 = w 1 ) and chiral (w 0 = 0) limits. We analytically show why going away from the isotropic limit by making w 0 less (but not larger) than w 1 increases the Γ M -point gap between the active and the passive bands. Finally, by perturbation theory, we provide an analytic Γ M point k ∙ p two-band model that reproduces the TBG band structure and eigenstates within a certain w 0 , w 1 parameter range. Further refinement of this model are discussed, which suggest a possible faithful representation of the TBG bands by a two-band Γ M point k ∙ p model in the full w 0 , w 1 parameter range.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1987

Uncertainty relations for light waves and the concept of photons

A Lorentz-covariant localization for light waves is presented. The unitary representation for the electromagnetic four-potential is constructed for a monochromatic light wave. A model for covariant superposition is constructed for light waves with different frequencies. It is therefore possible to construct a wave function for light waves carrying a covariant probability interpretation. It is shown that the time-energy uncertainty relation (Delta-t)(Delta-omega) = about 1 for light waves is a Lorentz-invariant relation. The connection between photons and localized light waves is examined critically.

Han, D.↗
NASA NTRS1993

Wavelets and spacetime squeeze

It is shown that the wavelet is the natural language for the Lorentz covariant description of localized light waves. A model for covariant superposition is constructed for light waves with different frequencies. It is therefore possible to construct a wave function for light waves carrying a covariant probability interpretation. It is shown that the time-energy uncertainty relation (Delta(t))(Delta(w)) is approximately 1 for light waves is a Lorentz-invariant relation. The connection between photons and localized light waves is examined critically.

Han, D.↗
DOE OSTI2020

Lattice QCD Calculations of Transverse-Momentum-Dependent Soft Function through Large-Momentum Effective Theory

The transverse-momentum-dependent (TMD) soft function is a key ingredient in QCD factorization of Drell-Yan and other processes with relatively small transverse momentum. We present a lattice QCD study of this function at moderately large rapidity on a 2 + 1 flavor CLS dynamic ensemble with a = 0.098 fm. We extract the rapidity-independent (or intrinsic) part of the soft function through a large-momentumtransfer pseudoscalar meson form factor and its quasi-TMD wave function using leading-order factorization in large-momentum effective theory. We also investigate the rapidity-dependent part of the soft function—the Collins-Soper evolution kernel—based on the large-momentum evolution of the quasi-TMD wave function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Performance of Diffusion Monte Carlo Calculations for Predicting the Relative Energies of Quinoidal and Nonquinoidal Species

Coupled cluster singles and doubles with perturbative triples [CCSD(T)] and single determinant fixed-node diffusion Monte Carlo (SD-DMC) have emerged as two of the most useful methods for providing benchmark reaction and interaction energies of chemical systems without strong static correlation. The errors in DMC energies are dominated by an inexact description of the nodal surfaces for electron exchange. One of the main approaches to addressing the fixed-node error is to use multideterminant (MD) trial wave functions. We consider here the energy differences between pairs of related molecules with aromatic and quinoidal structures as well as between quinoidal isomers. Quinoidal systems tend to have some diradical character, leading one to anticipate that SD-DMC calculations may face challenges in accurately describing their energetics. The MD trial wave functions were generated from the complete active space calculations. A comparison is made with the predictions of well-converged CCSD(T) calculations.

basis sets↗
DOE OSTI2024

Downfolding from ab initio to interacting model Hamiltonians: comprehensive analysis and benchmarking of the DFT+cRPA approach

Abstract Model Hamiltonians are regularly derived from first principles to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model system, here we carefully compare a standard downfolding technique with the best possible ground-truth estimates for charge-neutral excited-state energies and wave functions using state-of-the-art first-principles many-body wave function approaches. To this end, we use the vanadocene molecule and analyze all downfolding aspects, including the Hamiltonian form, target basis, double-counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double-counting corrections diminish the quality. Background screening of the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians.

Chemistry↗
NASA NTRS1986

Windows in direct dissociative recombination cross sections

Model potential curves are used to show that large windows are present in direct dissociative-recombination cross sections from excited molecular-ion vibrational levels. The windows are due to the overlap of vibrational wave functions of the repulsive neutral states with the nodes of the ion vibrational wave function.

Guberman, Steven L.↗
DOE OSTI2021

Examination of the sensitivity of quasifree reactions to details of the bound-state overlap functions

It is often stated that heavy-ion nucleon knockout reactions are mostly sensitive to the tails of the bound-state wave functions. In contrast, (p,2p) and (p,pn) reactions are known to access information on the full overlap functions within the nucleus. We analyze the oxygen isotopic chain and explore the differences between single-particle wave functions generated with potential models, used in the experimental analysis of knockout reactions, and ab initio computations from self-consistent Green's function theory. Contrary to common belief, we find that not only the tail of the overlap functions, but also their internal part is assessed in both reaction mechanisms, which are crucial to yield accurately determined spectroscopic information.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Color halo scenario of charmonium-like hybrids

The internal structures of J PC =1 -- ,(o,1,2) -+ charmonium-like hybrids are investigated under lattice QCD in the quenched approximation. We define the Bethe-Salpeter wave function (Φn(r)) in the Coulomb gauge as the matrix element of a spatially extended hybrid-like operator ($\bar{c}cg$) between the vacuum and n-th state for J PC , with r being the spatial separation between a localized $\bar{c}c$ component and the chromomagnetic strength tensor. These wave functions exhibit some similarities for states with the aforementioned different quantum numbers, and their r-behaviors (no node for the ground states and one node for the first excited states) imply that r can be a meaningful dynamical variable for these states. Additionally, the mass splittings of the ground states and first excited states of charmonium-like hybrids in these channels are obtained for the first time to be approximately 1.2-1.4 GeV. These results do not support the flux-tube description of heavy-quarkonium-like hybrids in the Born-Oppenheimer approximation. In contrast, a charmonium-like hybrid can be viewed as a "color halo" charmonium for which a relatively localized color octet $\bar{c}c$ is surrounded by gluonic degrees of freedom, which can readily decay into a charmonium state along with one or more light hadrons. The color halo picture is compatible with the decay properties of Y (42600) and suggests LHCb and BelleII to search for (0,1,2) -+ charmonium-like hybrids in Xc0,1,2N and J/ψω(φ) final states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Heavy-light mesons on the light front

Abstract We study the heavy-light mesons within basis light-front quantization. The resulting mass spectra of D , $$D_s$$ D s , B , and $$B_s$$ B s agree reasonably well with experiments. We also predict states which could be measured in the near future. In the light-front formalism, we calculate the light-front wave functions and additional experimental observables, such as parton distribution functions, distribution amplitudes, and decay constants by means of integrations over light-front wave functions. We also provide ratios of decay constants for selected pseudoscalar meson decays ( $$D_s$$ D s to D and $$B_s$$ B s to B ) as they may prove to be theoretically more robust and more reliably determined in experiments. We find that our ratios are systematically smaller than existing experiments and other approaches by 5–18%.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Glueballs at physical pion mass

Glueballs are investigated through gluonic operators on two $ N_f=2+1 $ RBC/UKQCD gauge ensembles at the physical pion mass. The statistical errors of glueball correlation functions are considerably reduced through the cluster decomposition error reduction (CDER) method. The Bethe-Salpeter wave functions are obtained for the scalar, tensor, and pseudoscalar glueballs by using spatially extended glueball operators defined through the gauge potential $ A_\mu(x) $ in the Coulomb gauge. These wave functions exhibit similar features of non-relativistic two-gluon systems and are used to optimize the signals of the related correlation functions at the early time regions, where the ground state masses are extracted. These masses are close to those from the quenched approximation and indicate the possible existence of glueballs at the physical point. The resonance feature of glueballs and the mixing with conventional mesons and multi-hadron systems should be considered in a more systematic lattice study.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

State Preparation in Quantum Algorithms for Fragment-Based Quantum Chemistry

State preparation for quantum algorithms is crucial for achieving high accuracy in quantum chemistry and competing with classical algorithms. The localized active space–unitary coupled cluster (LAS–UCC) algorithm iteratively loads a fragment-based multireference wave function onto a quantum computer. Here, in this study, we compare two state preparation methods, quantum phase estimation (QPE) and direct initialization (DI), for each fragment. We test the two state preparation methods on three systems, ranging from a model system, a set of interacting hydrogen molecules, to more realistic chemical problems, like the C–C double bond breaking in transbutadiene and the spin ladder in a bimetallic system. We analyze the impact of QPE parameters, such as the number of ancilla qubits and Trotter steps, on the prepared state. We find a trade-off between the methods, where DI requires fewer resources for smaller fragments, while QPE is more efficient for larger fragments. Our resource estimates highlight the benefits of system fragmentation in state preparation for subsequent quantum chemical calculations. These findings have broad applications for preparing multireference quantum chemical wave functions on quantum circuits that can be used for realistic chemical applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1986

Analysis of the physical atomic forces between noble gas atoms, alkali ions and halogen ions

The physical forces between atoms and molecules are important in a number of processes of practical importance, including line broadening in radiative processes, gas and crystal properties, adhesion, and thin films. The components of the physical forces between noble gas atoms, alkali ions, and halogen ions are analyzed and a data base for the dispersion forces is developed from the literature based on evaluations with the harmonic oscillator dispersion model for higher order coefficients. The Zener model of the repulsive core is used in the context of the recent asymptotic wave functions of Handler and Smith; and an effective ionization potential within the Handler and Smith wave functions is defined to analyze the two body potential data of Waldman and Gordon, the alkali-halide molecular data, and the noble gas crystal and salt crystal data. A satisfactory global fit to this molecular and crystal data is then reproduced by the model to within several percent. Surface potentials are evaluated for noble gas atoms on noble gas and salt crystal surfaces with surface tension neglected. Within this context, the noble gas surface potentials on noble gas and salt crystals are considered to be accurate to within several percent.

Wilson, J. W.↗
DOE OSTI2026

Jordan–Wigner Transformation for the Description of Strong Correlation in Fermionic Systems

Seniority is a useful way of organizing Hilbert space for strongly correlated systems. The exact zero-seniority wave function, doubly occupied configuration interaction (DOCI), provides accurate results (given the right orbitals) for many strongly correlated electronic systems but has a combinatorial computational cost. In many cases, pair coupled cluster doubles provide a polynomial-cost approximation that closely reproduces the energies of DOCI, but it breaks down in some cases and, as shown herein, it does not provide particularly good density matrices. In this article, we demonstrate that by using the Jordan–Wigner transformation to turn the seniority zero problem back into a Fermionic one, we can provide mean-field variational results of DOCI quality for the Hubbard model and a few small molecular dissociation examples, with polynomial cost, both for the energies and for density matrices, all while being protected from collapse. This success is rooted in the proof we provide, showing that the Hartree–Fock wave function on the Jordan–Wigner-transformed Hamiltonian transforms back to variational coupled cluster doubles in the seniority zero representation, but restricted to have determinant rather than permanent amplitude coefficients, without compromising its overall accuracy.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Chiral catalysis of nuclear fusion in molecules

At low energies, nuclear fusion is strongly affected by electron screening of the Coulomb repulsion among the fusing nuclei. It may thus be possible to catalyze nuclear fusion in molecules (i.e., to fuse specific nuclei in situ) through quantum control of electron wave functions in intense laser fields. The circularly polarized (chiral) laser field can effectively squeeze the electron wave functions, greatly enhancing the screening in the spatial region relevant for the fusion process. Here, we estimate the corresponding fusion probabilities, and find that the proposed chiral catalysis of nuclear fusion in molecules may be observable, potentially with important practical applications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Response Functions of Correlated Systems within Green's Function Theory

Why use Green's functions as the fundamental variable? Wave-function (Psi) methods are king for high-fidelity and Density-functional (Rho) methods are very efficient (Kohn-Sham). Goldilocks principle: Green's function (G) methods straddle the Rho and Psi methods, intermediate in both accuracy and efficiency. Also, when interest lies in excitations & 2-particle properties: G-methods are natural - intrinsic to the theory.

DMFT↗
NASA NTRS2004

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition: Inclusion of Exchange - 2

The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.

Shertzer, Janine↗