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Results for “Hamiltonian Monte Carlo”

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.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Starting-point-independent quantum Monte Carlo calculations of iron oxide

Quantum Monte Carlo (QMC) methods are useful for studies of strongly correlated materials because they are many body in nature and use the physical Hamiltonian. Typical calculations assume as a starting point a wave function constructed from single-particle orbitals obtained from one-body methods, e.g., density functional theory. However, mean-field-derived wave functions can sometimes lead to systematic QMC biases if the mean-field result poorly describes the true ground state. In this study, we examine the accuracy and flexibility of QMC trial wave functions using variational and fixed-node diffusion QMC estimates of the total spin density and lattice distortion of antiferromagnetic iron oxide (FeO) in the ground state B1 crystal structure. We found that for relatively simple wave functions the predicted lattice distortion was controlled by the choice of single-particle orbitals used to construct the wave function, rather than by subsequent wave function optimization techniques within QMC. By optimizing the orbitals with QMC, we then demonstrate starting-point independence of the trial wave function with respect to the method by which the orbitals were constructed by demonstrating convergence of the energy, spin density, and predicted lattice distortion for two qualitatively different sets of orbitals. The results suggest that orbital optimization is a promising method for accurate many-body calculations of strongly correlated condensed phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Finite-Temperature Structures of Supported Subnanometer Catalysts Inferred via Statistical Learning and Genetic Algorithm-Based Optimization

Single-atom catalysts (SACs) minimize noble metal utilization and can alter the activity and selectivity of supported metal nanoparticles. However, the morphology of active centers, including single atoms and subnanometer clusters of a few atoms, remains elusive due to experimental challenges. The computational cost to describe numerous cluster shapes and sizes makes direct first-principles calculations impractical. We present a computational framework to enable structure determination for single-atom and subnanometer cluster catalysts. As a case study, we obtained the low energy structures of Pd n (n = 1-21) clusters supported on CeO 2 (111), which are critical components of automobile three-way catalysts. Trained on density functional theory data, a three-dimensional cluster expansion is established using statistical learning to describe the Hamiltonian and predict energies of supported Pdn clusters of any structure. Low energy stable and metastable structures are identified using a Metropolis Monte Carlo-based genetic algorithm in the canonical ensemble at 300 K. We observe that supported single atoms sinter to form bilayer clusters and large cluster isomers share similarities in both shape and energy, and elucidate the significance of the support and microstructure on cluster stability. We discovered a simple surrogate structure-energy model, where the energy per atom scales with the square root of the average first coordination number, which can be used to estimate energies and compare the stability of clusters. Our framework, applicable to any metal/support system, fills an important methodological gap to predict the stability of supported metal catalysts in the subnanometer regime.

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

Effect of emitters on quantum state transfer in coupled cavity arrays

Over the last decade, conditions for perfect state transfer in quantum spin chains have been discovered and their experimental realizations addressed, as have their extensions to more complex geometries of coupled cavity-emitter arrays. In this paper we further consider such studies and situations in which quantum state transfer can occur with high fidelity, even when the cavity-cavity coupling rates and cavity-emitter interaction rates are comparable. This is accomplished through the development and use of a Monte Carlo approach to the inverse eigenvalue problem, which allows the determination of coupling rates which optimize quantum state transfer fidelity and subsequent time evolution of the polariton wave function through exact diagonalization of the resulting Jaynes-Cummings-Hubbard Hamiltonian. The effect of inhomogeneous emitter locations is also evaluated. Furthermore, our key results include the demonstration that our methodology can be used successfully to establish Hamiltonian parameters for high-fidelity state transfer in more general lattice geometries and excitation number sectors, and also a determination of the effects of fluctuations in those parameters about their optimal values.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics

Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman–von Neumann formulation of classical mechanics. The Koopman–von Neumann formulation implies that the conservation of the probability distribution function on phase space, as expressed by the Liouville equation, can be recast as an equivalent Schrödinger equation on Hilbert space with a Hermitian Hamiltonian operator and a unitary propagator. This Schrödinger equation is linear in the momenta because it derives from a constrained Hamiltonian system with twice the classical phase-space dimension. A quantum computer with finite resources can be used to simulate a finite-dimensional approximation of this unitary evolution operator. Quantum simulation of classical dynamics is exponentially more efficient than a deterministic Eulerian discretization of the Liouville equation if the Koopman–von Neumann Hamiltonian is sparse. Utilizing quantum walk techniques for state preparation and amplitude estimation for the calculation of observables leads to a quadratic improvement over classical probabilistic Monte Carlo algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Distilling the Essential Elements of Nuclear Binding via Neural-Network Quantum States

To distill the essential elements of nuclear binding, we seek the simplest Hamiltonian capable of modeling atomic nuclei with percent-level accuracy. A critical aspect of this endeavor consists of accurately solving the quantum many-body problem without incurring an exponential computing cost with the number of nucleons. Furthermore, we address this challenge by leveraging a variational Monte Carlo method based on a highly expressive neural-network quantum state ansatz. In addition to computing binding energies and charge radii of nuclei with up to 𝐴 = 20 nucleons, by evaluating their magnetic moments, we demonstrate that neural-network quantum states are able to correctly capture the self-emerging nuclear shell structure. To this end, we introduce a novel computational protocol based on adding an external magnetic field to the nuclear Hamiltonian, which allows the neural network to learn the preferred polarization of the nucleus within the given magnetic field.

Binding energy & masses↗
DOE OSTI2020

Spin response and neutrino mean free path in neutron matter

The longitudinal and transverse density- and spin-density response functions in pure neutron matter (PNM) are derived over a wide range of densities within the time dependent local spin density approximation. The underlying density functional was derived from an Auxiliary Field Diffusion Monte Carlo computation of the equation of state of unpolarized and fully spin polarized PNM. In order to assess the dependence of the results on the specific underlying nucleon–nucleon Hamiltonian, we used both the phenomenological Argonne AV8' + UIX force, and local chiral forces up to next-to-next-to-leading-order (N 2 LO). Finally, the resulting response function has then been applied to the study of the neutrino mean free path in PNM.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Perturbative Quantum Monte Carlo Method for Nuclear Physics

While first order perturbation theory is routinely used in quantum Monte Carlo (QMC) calculations, higher-order terms present significant numerical challenges. We present a new approach for computing perturbative corrections in projection QMC calculations. Here we demonstrate the method by computing nuclear ground state energies up to second order for a realistic chiral interaction. We calculate the binding energies of several light nuclei up to 16 O by expanding the Hamiltonian around the Wigner SU(4) limit and find good agreement with data. In contrast to the natural ordering of the perturbative series, we find remarkably large second-order energy corrections. This occurs because the perturbing interactions break the symmetries of the unperturbed Hamiltonian. Our method is free from the sign problem and can be applied to QMC calculations for many-body systems in nuclear physics, condensed matter physics, ultracold atoms, and quantum chemistry.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Pulse-level noisy quantum circuits with QuTiP

The study of the impact of noise on quantum circuits is especially relevant to guide the progress of Noisy Intermediate-Scale Quantum (NISQ) computing. In this paper, we address the pulse-level simulation of noisy quantum circuits with the Quantum Toolbox in Python (QuTiP). We introduce new tools in qutip-qip, QuTiP's quantum information processing package. These tools simulate quantum circuits at the pulse level, leveraging QuTiP's quantum dynamics solvers and control optimization features. We show how quantum circuits can be compiled on simulated processors, with control pulses acting on a target Hamiltonian that describes the unitary evolution of the physical qubits. Various types of noise can be introduced based on the physical model, e.g., by simulating the Lindblad density-matrix dynamics or Monte Carlo quantum trajectories. In particular, the user can define environment-induced decoherence at the processor level and include noise simulation at the level of control pulses. We illustrate how the Deutsch-Jozsa algorithm is compiled and executed on a superconducting-qubit-based processor, on a spin-chain-based processor and using control optimization algorithms. We also show how to easily reproduce experimental results on cross-talk noise in an ion-based processor, and how a Ramsey experiment can be modeled with Lindblad dynamics. Finally, we illustrate how to integrate these features with other software frameworks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Advanced measurement techniques in quantum Monte Carlo: The permutation matrix representation approach

In a typical finite temperature quantum Monte Carlo (QMC) simulation, estimators for simple static observables such as specific heat and magnetization are known. With a great deal of system-specific manual labor, one can sometimes also derive more complicated non-local or even dynamic observable estimators. In contrast, we show that arbitrary static observables can be estimated within the permutation matrix representation (PMR) flavor for any Hamiltonian. We then generalize these results to general imaginary-time correlation functions and non-trivial integrated susceptibilities thereof. Finally, we demonstrate the practical versatility of our method by estimating various non-local, random observables for the transverse-field Ising model on a square lattice and a toy random model.

Permutation matrix representation↗
DOE OSTI2021

25 Siβ + -decay spectroscopy

Background: β-decay spectroscopy provides valuable information on exotic nuclei and a stringent test for nuclear theories beyond the stability line. Purpose: To search for new β-delayed protons and γ rays of 25 Si to investigate the properties of 25 Al excited states. Method: 25 Si β decays were measured by using the Gaseous Detector with Germanium Tagging system at the National Superconducting Cyclotron Laboratory. The protons and γ rays emitted in the decay were detected simultaneously. Here, a Monte Carlo method was used to model the Doppler broadening of 24 Mg γ-ray lines caused by nuclear recoil from proton emission. Shell-model calculations using two newly developed universal sd-shell Hamiltonians were performed. Results: The most precise 25Si half-life to date has been determined. A new proton branch at 724(4) keV and new proton-γ-ray coincidences have been identified. Three 24 Mg γ-ray lines and eight 25 Al γ-ray lines are observed for the first time in 25 Si decay. The first measurement of the 25 Si β-delayed γ-ray intensities through the 25 Al unbound states is reported. All the bound states of 25 Al are observed to be populated in the β decay of 25 Si. Several inconsistencies between the previous measurements have been resolved, and new information on the 25 Al level scheme is provided. An enhanced decay scheme has been constructed and compared to the mirror decay of 25 Na and the shell-model calculations. Conclusions: The measured excitation energies, γ-ray and proton branchings, log $ft$ values, and Gamow-Teller transition strengths for the states of 25 Al populated in the β decay of 25 Si are in good agreement with the shell model calculations, offering gratifyingly consistent insights into the fine nuclear structure of 25 Al.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

The 1 S 0 Pairing Gap in Neutron Matter

We report ab initio calculations of the S wave pairing gap in neutron matter calculated using realistic nuclear Hamiltonians that include two- and three-body interactions. We use a trial state, properly optimized to capture the essential pairing correlations, from which we extract ground state properties by means of auxiliary field diffusion Monte Carlo simulations. We extrapolate our results to the thermodynamic limit by studying the finite-size effects in the symmetry-restored projected Bardeen-Cooper-Schrieffer (PBCS) theory and compare our results to other ab initio studies done in the past. Our quantum Monte Carlo results for the pairing gap show a modest suppression with respect to the mean-field BCS values. These results can be connected to cold atom experiments, via the unitarity regime where fermionic superfluidity assumes a unified description, and they are important in the prediction of thermal properties and the cooling of neutron stars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Ab initio calculations in atoms, molecules, and solids, treating spin–orbit coupling and electron interaction on an equal footing

We incorporate explicit, non-perturbative treatment of spin–orbit coupling into ab initio auxiliary-field quantum Monte Carlo (AFQMC) calculations. The approach allows a general computational framework for molecular and bulk systems in which material specificity, electron correlation, and spin–orbit coupling effects can be captured accurately and on an equal footing, with favorable computational scaling vs system size. We adopt relativistic effective-core potentials that have been obtained by fitting to fully relativistic data and that have demonstrated a high degree of reliability and transferability in molecular systems. This results in a two-component spin-coupled Hamiltonian, which is then treated by generalizing the ab initio AFQMC approach. We demonstrate the method by computing the electron affinity in Pb, the bond dissociation energy in Br 2 and I 2 , and solid Bi.

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

Benchmark calculations of infinite neutron matter with realistic two- and three-nucleon potentials

In this study, we present the equation of state of infinite neutron matter as obtained from highly realistic Hamiltonians that include nucleon-nucleon and three-nucleon coordinate-space potentials. We benchmark three independent many-body methods: Brueckner-Bethe-Goldstone (BBG), Fermi hypernetted chain/single-operator chain (FHNC/SOC), and auxiliary-field diffusion Monte Carlo (AFDMC). We find them to provide similar equations of state when the Argonne v 18 and the Argonne v' 6 nucleon-nucleon potentials are used in combination with the Urbana IX three-body force. Only at densities larger than about 1.5 the nuclear saturation density ( ρ 0 =0.16 fm ⁻3 ) the FHNC/SOC energies are appreciably lower than the other two approaches. The AFDMC calculations carried out with all of the Norfolk potentials fitted to reproduce the experimental trinucleon ground-state energies and nd doublet scattering length yield unphysically bound neutron matter, associated with the formation of neutron droplets. Including tritium β decay in the fitting procedure, as in the second family of Norfolk potentials, mitigates but does not completely resolve this problem. An excellent agreement between the BBG and AFDMC results is found for the subset of Norfolk interactions that do not make neutron-matter collapse, while the FHNC/SOC equations of state are moderately softer.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Multiple incommensurate magnetic states in the kagome antiferromagnet Na 2 Mn 3 Cl 8

The kagome lattice can host exotic magnetic phases arising from frustrated and competing magnetic interactions. However, relatively few insulating kagome materials exhibit incommensurate magnetic ordering. Here, we present a study of the magnetic structures and interactions of antiferromagnetic Na 2 Mn 3 Cl 8 with an undistorted Mn 2+ kagome network. Using neutron-diffraction and bulk magnetic measurements, we show that Na 2 Mn 3 Cl 8 hosts two different incommensurate magnetic states, which develop at T N1 = 1.6 K and T N2 = 0.6 K. Magnetic Rietveld refinements indicate magnetic propagation vectors of the form q=(q x , q y , $\frac{3}{2}$), and our neutron-diffraction data can be well described by cycloidal magnetic structures. By optimizing exchange parameters against magnetic diffuse-scattering data, we show that the spin Hamiltonian contains ferromagnetic nearest-neighbor and antiferromagnetic third-neighbor Heisenberg interactions, with a significant contribution from long-ranged dipolar coupling. This experimentally determined interaction model is compared with density-functional-theory simulations. Using classical Monte Carlo simulations, we show that these competing interactions explain the experimental observation of multiple incommensurate magnetic phases and may stabilize multi-q states. Here, our results expand the known range of magnetic behavior on the kagome lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model

Determining the range of validity of Migdal’s approximation for electron-phonon (e-ph) coupled systems is a long-standing problem. Many attempts to answer this question employ the Holstein Hamiltonian, where the electron density couples linearly to local lattice displacements. When these displacements are large, however, nonlinear corrections to the interaction must also be included, which can significantly alter the physical picture obtained from this model. Using determinant quantum Monte Carlo and the self-consistent Migdal approximation, we compared superconducting and charge-density-wave correlations in the Holstein model with and without second-order nonlinear interactions. We find a disagreement between the two cases, even for relatively small values of the e-ph coupling strength, and, importantly, that this can occur in the same parameter regions where Migdal’s approximation holds. Our results demonstrate that questions regarding the validity of Migdal’s approximation go hand in hand with questions of the validity of a linear e-ph interaction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Maximally local two-nucleon interactions at N 3 LO in Δ -less chiral effective field theory

We present new maximally local two-nucleon interactions derived in Δ -less chiral effective field theory up to next-to-next-to-next-to-leading order ( N 3 LO ), which include all contact and pion-exchange contributions to the nuclear Hamiltonian up to this order. Our interactions are fit to nucleon-nucleon phase shifts using a Bayesian statistical approach, and explore a wide cutoff range from 0.6 – 0.9 fm ( ≈ 660 – 440 MeV ). These interactions can be straightforwardly employed in quantum Monte Carlo methods, such as the auxiliary field diffusion Monte Carlo method. Together with local three-nucleon forces, calculations with these new interactions will provide improved benchmarks for the structure of atomic nuclei and serve as crucial input to analyses of astrophysical phenomena of neutron stars, such as binary neutron-star mergers. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Krylov spaces for truncated spectrum methodologies

We propose herein an extension of truncated spectrum methodologies, a nonperturbative numerical approach able to elucidate the low energy properties of quantum field theories. TSMs, in their various flavors, involve a division of a computational Hilbert space, H , into two parts, one part, H 1 that is “kept” for the numerical computations, and one part, H 2 , that is discarded or “truncated.” Even though H 2 is discarded, truncated spectrum methodologies will often try to incorporate the effects of H 2 in some effective way. In these terms, we propose to keep the dimension of H 1 small. We pair this choice of H 1 with a Krylov subspace iterative approach able to take into account the effects of H 2 . This iterative approach can be taken to arbitrarily high order and so offers the ability to compute quantities to arbitrary precision. In many cases it also offers the advantage of not needing an explicit UV cutoff. To compute the matrix elements that arise in the Krylov iterations, we employ a Feynman diagrammatic representation that is then evaluated with Monte Carlo techniques. Each order of the Krylov iteration is variational and is guaranteed to improve upon the previous iteration. The first Krylov iteration is akin to the next-to-leading order approach of Elias-Miró [NLO renormalization in the Hamiltonian truncation, ]. To demonstrate this approach, we focus on the ( 1 + 1 d )-dimensional ϕ 4 model and compute the bulk energy and mass gaps in both the Z 2 -broken and unbroken sectors. We estimate the critical ϕ 4 coupling in the broken phase to be g c = 0.2645 ± 0.002 . Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗