Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “density matrix methods”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

What is the Best Alternative to Diagonalization of the Hamiltonian in Large Scale Semiempirical Calculations?

Recently, several linear scaling approaches have been introduced which replace the time dominating diagonalization step in semiempirical methods, enabling practical calculations to be performed, on very large molecules. This paper compares the accuracy and performance of pseudodiagonalization (PD), conjugate gradient density matrix search (CG-DMS), the Chebyshev polynomial expansion method (CEM), and purification of the density matrix (PDM) as linear scaling substitutions for diagonalization. The scaling, speed, and reliability of these methods are compared for AMI single point energy calculations on polyglycine chains (up to 20,000 atoms), water clusters (up to 12,300 atoms), and nucleic acids (up to 6300 atoms).

Daniels, Andrew D.↗
DOE OSTI2020

Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation

It is shown how the electronic equations of motion in extended Lagrangian Born–Oppenheimer molecular dynamics simulations can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born–Oppenheimer molecular dynamics. We note the low-rank approximation of the Jacobian is directly related to Broyden’s class of quasi-Newton algorithms and Jacobian-free Newton–Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Finite-size subthermal regime in disordered SU ( N ) -symmetric Heisenberg chains

SU⁡(N) symmetry is incompatible with the many-body localized (MBL) phase, even when strong disorder is present. However, recent studies have shown that finite-size SU⁡(2) systems exhibit nonergodic, subthermal behavior, characterized by the breakdown of the eigenstate thermalization hypothesis, and by the excited eigenstates entanglement entropy that is intermediate between area and volume law. In this paper, we extend previous studies of the SU⁡(2)-symmetric disordered Heisenberg model to larger systems, using the time-dependent density matrix renormalization group (tDMRG) method. We simulate quench dynamics from weakly entangled initial states up to long times, finding robust subthermal behavior at stronger disorder. Although we find an increased tendency towards thermalization at larger system sizes, the subthermal regime persists at intermediate time scales, nevertheless, and therefore should be accessible experimentally. At weaker disorder, we observe signatures of thermalization; however, entanglement entropy exhibits slow sublinear growth, in contrast to conventional thermalizing systems. Furthermore, we study dynamics of the SU⁡(3)-symmetric disordered Heisenberg model. Similarly, strong disorder drives the system into subthermal regime, albeit thermalizing phase is broader compared to the SU⁡(2) case. Finally, our findings demonstrate the robustness of the subthermal regime in spin chains with non-Abelian continuous symmetry, and are consistent with eventual thermalization at large system sizes and long time scales, suggested by previous studies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Rethinking 𝛼−RuCl 3 : Parameters, models, and phase diagram

RuCl 3 was likely the first ever deliberately synthesized ruthenium compound, following the discovery of the 44 Ru element in 1844. For a long time it was known as an oxidation catalyst, with its physical properties being discrepant and confusing, until a decade ago when its allotropic form 𝛼−RuCl 3 rose to exceptional prominence. This “rediscovery” of 𝛼−RuCl 3 has not only reshaped the hunt for a material manifestation of the Kitaev spin liquid, but it has opened the floodgates of theoretical and experimental research in the many unusual phases and excitations that the anisotropic-exchange magnets as a class of compounds have to offer. Given its importance for the field of Kitaev materials, it is astonishing that the low-energy spin model that describes this compound and its possible proximity to the much-desired spin-liquid state is still a subject of significant debate ten years later. In the present study, we argue that the existing key phenomenological observations put strong natural constraints on the effective microscopic spin model of 𝛼−RuCl 3 , and specifically on its spin-orbit-induced anisotropic-exchange parameters that are responsible for the nontrivial physical properties of this material. These constraints allow one to focus on the relevant region of the multidimensional phase diagram of the 𝛼−RuCl 3 model, suggest an intuitive description of it via a different parametrization of the exchange matrix, offer a unifying view on the earlier assessments of its parameters, and bring closer together several approaches to the derivation of anisotropic-exchange models. We explore extended phase diagrams relevant to the 𝛼−RuCl 3 parameter space using quasiclassical, Luttinger-Tisza, exact diagonalization, and density-matrix renormalization-group methods, demonstrating a remarkably close quantitative accord between them on the general structure and hierarchy of the phases, with the zigzag, ferromagnetic, and incommensurate phases that are proximate to each other. As a result, one of the highlights is the detailed agreement on the nature of the incommensurate phases that realize two distinct counterrotating helical states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Doped Mott insulators in the triangular-lattice Hubbard model

Here we investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping δ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping δ ≲ 10%, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well-defined Fermi surface. On further doping, δ ≈ 10%~20% SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping δ ≳ 20%, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Tracing the Mott-Hubbard transition in one-dimensional Hubbard models without Umklapp scattering

Here we apply the density-matrix renormalization group (DMRG) method to a one-dimensional Hubbard model that lacks Umklapp scattering and thus provides an ideal case to study the Mott-Hubbard transition analytically and numerically. The model has a linear dispersion and displays a metal-to-insulator transition when the Hubbard interaction U equals the bandwidth U c = W, where the single-particle gap opens linearly, Δ(U ≥ W) = U - W. The simple nature of the elementary excitations permits us to determine numerically with high accuracy the critical interaction strength and the gap function in the thermodynamic limit. The jump discontinuity of the momentum distribution $n_k$ at the Fermi wave number $k_F$ = 0 cannot be used to locate accurately U c from finite-size systems. However, the slope of $n_k$ at the band edges $k_B$ = ±π, reveals the formation of a single-particle bound state which can be used to determine U c reliably from $n_k$ using accurate finite-size data.

1-dimensional systems↗
DOE OSTI2021

Equation-of-motion coupled-cluster method with double electron-attaching operators: Theory, implementation, and benchmarks

We report a production-level implementation of the equation-of-motion (EOM) coupled-cluster (CC) method with double electron-attaching (DEA) EOM operators of 2 p and 3 p 1 h types, EOM-DEA-CCSD. This ansatz, suitable for treating electronic structure patterns that can be described as two-electrons-in-many orbitals, represents a useful addition to the EOM-CC family of methods. We analyze the performance of EOM-DEA-CCSD for energy differences and molecular properties. By considering reduced quantities, such as state and transition one-particle density matrices, we compare EOM-DEA-CCSD wave functions with wave functions computed by other EOM-CCSD methods. The benchmarks illustrate that EOM-DEA-CCSD is capable of treating diradicals, bond-breaking, and some types of conical intersections.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Sub-system self-consistency in coupled cluster theory

Here, in this article, we provide numerical evidence indicating that the single-reference coupled-cluster (CC) energies can be calculated alternatively to their copybook definition. We demonstrate that the CC energy can be reconstructed by diagonalizing the effective Hamiltonians describing correlated sub-systems of the many-body system. In the extreme case, we provide numerical evidence that the CC energy can be reproduced through the diagonalization of the effective Hamiltonian describing sub-system composed of a single electron. These properties of the CC formalism can be exploited to design protocols to define effective interactions in sub-systems used as probes to calculate the energy of the entire system and introduce a new type of self-consistency for approximate CC approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

N -representability violations in truncated equation-of-motion coupled-cluster methods

One-electron reduced density matrices (1RDMs) from equation-of-motion (EOM) coupled-cluster with single and double excitations (CCSD) calculations are analyzed to assess their N-representability (i.e., whether they are derivable from a physical N-electron state). We identify EOM-CCSD stationary states whose 1RDMs violate either ensemble-state N-representability conditions or pure-state conditions known as generalized Pauli constraints. As such, these 1RDMs do not correspond to any physical N-electron state. Unphysical states are also encountered in the course of time-dependent EOM-CC simulations; when an external field drives transitions between a pair of stationary states with pure-state N-representable 1RDMs, the 1RDM of the time-dependent state can violate ensemble-state conditions. Furthermore, these observations point to potential challenges in interpreting the results of time-dependent EOM-CCSD simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

On-the-fly machine learned force fields for the study of warm dense matter: Application to diffusion and viscosity of CH

We develop a framework for on-the-fly machine learned force field (MLFF) molecular dynamics (MD) simulations of warm dense matter (WDM). In particular, we employ an MLFF scheme based on the kernel method and Bayesian linear regression, with the training data generated from the Kohn–Sham density functional theory (DFT) using the Gauss spectral quadrature method, within which we calculate energies, atomic forces, and stresses. We verify the accuracy of the formalism by comparing the predicted properties of warm dense carbon with recent Kohn–Sham DFT results in the literature. In so doing, we demonstrate that ab initio MD simulations of WDM can be accelerated by up to three orders of magnitude, while retaining ab initio accuracy. We apply this framework to calculate the diffusion coefficients and shear viscosity of CH at a density of 1 g/cm3 and temperatures in the range of 75 000–750 000 K. We find that the self- and inter-diffusion coefficients and the viscosity obey a power law with temperature, and that the diffusion coefficient results suggest a weak coupling between C and H in CH. In addition, we find agreement within standard deviation with previous results for C and CH but disagreement for H, demonstrating the need for ab initio calculations as presented here.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

A static quantum embedding scheme based on coupled cluster theory

Here, we develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To reduce the computational cost, we solve the local fragment problem using a high-level CC method and address the environment problem with a lower-level Møller–Plesset (MP) perturbative method. This embedding approach inherits many conceptual developments from the hybrid second-order Møller–Plesset (MP2) and CC works by Nooijen [J. Chem. Phys. 111, 10815 (1999)] and Bochevarov and Sherrill [J. Chem. Phys. 122, 234110 (2005)]. We go beyond those works here by primarily targeting a specific localized fragment of a molecule and also introducing an alternative mechanism to relax the environment within this framework. We will call this approach MP-CC. We demonstrate the effectiveness of MP-CC on several potential energy curves and a set of thermochemical reaction energies, using CC with singles and doubles as the fragment solver, and MP2-like treatments of the environment. The results are substantially improved by the inclusion of orbital relaxation in the environment. Using localized bonds as the active fragment, we also report results for N=N bond breaking in azomethane and for the central C–C bond torsion in butadiene. We find that when the fragment Hilbert space size remains fixed (e.g., when determined by an intrinsic atomic orbital approach), the method achieves comparable accuracy with both a small and a large basis set. Additionally, our results indicate that increasing the fragment Hilbert space size systematically enhances the accuracy of observables, approaching the precision of the full CC solver.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Exact matrix product state representation and convergence of a fully correlated electronic wavefunction in the infinite-basis limit

Here In this paper we present the exact representation of a fully correlated electronic wavefunction as the single-particle basis approaches completeness. It consists of a half-infinite chain of matrices of exponentially increasing size. The complete basis limit is illustrated numerically using the density-matrix renormalization-group method by computing the core-valence entanglement in the C 2 ground state in increasing subsets of cc-pVTZ and pVQZ bases until convergence is reached.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Nature of quantum spin liquids of the S = 1 2 Heisenberg antiferromagnet on the triangular lattice: A parallel DMRG study

Here we study the ground-state properties of the quantum spin liquid (QSL) phases of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice with nearest- (J 1 ), next-nearest- (J 2 ), and third-neighbor (J 3 ) interactions by using density-matrix renormalization group (DMRG) method. By combining parallel DMRG with SU(2) spin rotational symmetry, we are able to obtain accurate results on large cylinders with length up to L x =48 and circumference L y =6–12. Our results suggest that the QSL phase of the J 1 -J 2 Heisenberg model is gapped which is characterized by the absence of gapless mode, short-range spin-spin and dimer-dimer correlations. In the presence of J 3 interaction, we find that a new critical QSL with a single gapless mode emerges. While both spin-spin and scalar chiral-chiral correlations are short-ranged, dimer-dimer correlations are quasi-long-ranged which decays as a power-law at long distances.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Influence of extended interactions on spin dynamics in one-dimensional cuprates

Quasi-one-dimensional (1D) materials provide a unique platform for understanding the importance and influence of extended interactions on the physics of strongly correlated systems due to their relative structural simplicity and the existence of powerful theoretical tools well-adapted to one spatial dimension. Recently, this was highlighted by anomalous observations in the single-particle spectral function A(q, ω) of 1D cuprate chain compounds, measured by angle-resolved photoemission spectroscopy (ARPES), which were explained by the presence of a long-range attractive interaction. Such an extended interaction should leave its fingerprints on other observables, notably the dynamical spin structure factor S(q, ω), measured by neutron scattering or resonant inelastic x-ray scattering (RIXS). Starting from a simple Hubbard Hamiltonian in 1D and using time-dependent density matrix renormalization group (tDMRG) methods, we show that the presence of long-range attractive coupling, directly through an instantaneous Coulomb interaction V or retarded electron phonon (el-ph) coupling, can introduce significant spectral weight redistribution in S(q, ω) across a wide range of doping. Here, this underscores the significant impact that extended interactions can have on dynamical correlations among particles, and the importance of properly incorporating this influence in modeling. Our results demonstrate that S(q, ω) can provide a sensitive experimental constraint, which complements ARPES measurements, in identifying key interactions in 1D cuprates, beyond the standard Hubbard model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Density matrix renormalization group description of the island of inversion isotopes F 28 – 33

Recent experiments have confirmed that the neutron-rich isotopes 28,29 F belong to the so-called island of inversion (IOI), a region of the nuclear chart around Z = 10 and N = 20 where nuclear structure deviates from the standard shell model predictions due to deformation and continuum effects. However, while the general principles leading to the IOI are relatively well understood, the details of the low-lying structure of the exotic fluorine isotopes 28–33 F are basically unknown. In this study, we perform large-scale shell model calculations including continuum states to investigate the properties of the neutron-rich isotopes 25–33 F, from a core of 24 O and using an effective two-body interaction with a small number of adjustable parameters in the central and tensor channels. We develop two models adjusted on experimentally confirmed states in 25,26 O and 25–27 F based on different assumptions concerning the positions of the neutron 0d 3/2 and 1p 3/2 shells, and solve the many-body problem using the density matrix renormalization group (DMRG) method for open quantum systems in an sd–fp model space. We obtain the first detailed spectroscopy of 25–33F in the continuum and show how the interplay between continuum effects and deformation explains the recent data on 28,29 F. Several deformed one- and two-neutron halo states are predicted in 29,31 F, and we provide some information about the possible structure of the heaviest fluorine isotopes. We also suggest several experimental studies of interest to constraint models and test the present predictions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Room-Temperature Mechanical Resonator with a Single Added or Subtracted Phonon

A room-temperature mechanical oscillator undergoes thermal Brownian motion with an amplitude much larger than the amplitude associated with a single phonon of excitation. This motion can be read out and manipulated using laser light using a cavity-optomechanical approach. By performing a strong quantum measurement (i.e., counting single photons in the sidebands imparted on a laser), we herald the addition and subtraction of single phonons on the 300 K thermal motional state of a 4 GHz mechanical oscillator. Further, to understand the resulting mechanical state, we implement a tomography scheme and observe highly non-Gaussian phase-space distributions. Using a maximum likelihood method, we infer the density matrix of the oscillator, and we confirm the counterintuitive doubling of the mean phonon number resulting from phonon addition and subtraction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗