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Results for “Path-integral 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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16 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Melting curves of atomic hydrogen and deuterium calculated using path-integral Monte Carlo

We calculate the melting line of atomic hydrogen and deuterium up to 900 GPa with path-integral Monte Carlo using a machine-learned interatomic potential. We improve upon previous simulations of melting by treating the electrons with reptation quantum Monte Carlo, and by performing solid and liquid simulations using isothermal-isobaric path-integral Monte Carlo. Here, the resulting melting line for atomic hydrogen is higher than previous estimates. There is a small but resolvable decrease in the melting temperature as pressure is increased, which can be attributed to quantum effects.

08 HYDROGEN↗
DOE OSTI2021

Nucleon clustering at kinetic freezeout of heavy-ion collisions via path-integral Monte Carlo

Clustering of the four-nucleon system at kinetic freezeout conditions is studied using path-integral Monte Carlo techniques. This method seeks to improve upon previous calculations which relied on approximate semiclassical methods or few-body quantum mechanics. Estimates are given for the decay probabilities of the 4N system into various light nuclei decay channels and the strength of spatial correlations is characterized. Additionally, a simple model is presented to describe the impact of this clustering on nucleon multiplicity distributions. Additionally, the effects of a possible modification of the inter-nucleon interaction due to the close critical line (and hypothetical QCD critical point) on the clustering are also studied.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Electronic density response of warm dense matter

Matter at extreme temperatures and pressures—commonly known as warm dense matter (WDM)—is ubiquitous throughout our Universe and occurs in astrophysical objects such as giant planet interiors and brown dwarfs. Moreover, WDM is very important for technological applications such as inertial confinement fusion and is realized in the laboratory using different techniques. A particularly important property for the understanding of WDM is given by its electronic density response to an external perturbation. Such response properties are probed in x-ray Thomson scattering (XRTS) experiments and are central for the theoretical description of WDM. In this work, we give an overview of a number of recent developments in this field. To this end, we summarize the relevant theoretical background, covering the regime of linear response theory and nonlinear effects, the fully dynamic response and its static, time-independent limit, and the connection between density response properties and imaginary-time correlation functions (ITCF). In addition, we introduce the most important numerical simulation techniques, including path-integral Monte Carlo simulations and different thermal density functional theory (DFT) approaches. From a practical perspective, we present a variety of simulation results for different density response properties, covering the archetypal model of the uniform electron gas and realistic WDM systems such as hydrogen. Moreover, we show how the concept of ITCFs can be used to infer the temperature from XRTS measurements of arbitrary complex systems without the need for any models or approximations. Finally, we outline a strategy for future developments based on the close interplay between simulations and experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Negative string tension of a higher-charge Schwinger model via digital quantum simulation

We study some properties of generalized global symmetry for the charge- q Schwinger model in the Hamiltonian formalism, which is the (1 + 1)D quantum electrodynamics with a charge- q Dirac fermion. This model has the |$\mathbb {Z}_q\, 1$| -form symmetry, which is a remnant of the electric |$U(1)\, 1$| -form symmetry in the pure Maxwell theory. It is known that, if we put the theory on closed space, then the Hilbert space is decomposed into q distinct sectors, called universes, and some states with higher energy density do not decay to the ground state due to the selection rule of the 1-form symmetry. Even with open boundaries, we can observe the stability of such states by seeing a negative string tension behavior, meaning that opposite charges repel each other. In order to see negative string tensions, the vacuum angle θ has to be large enough and the standard path-integral Monte Carlo method suffers from the sign problem. We develop a method based on the adiabatic state preparation to see this feature with digital quantum simulation and confirm it using a classical simulator of quantum devices. In particular, we measure the local energy density and see how it jumps between the inside and outside of the insertion of the probe charges. We explicitly see that the energy density inside is lower than that outside. This is a clear signature of the negative string tension.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Stable Solid Molecular Hydrogen above 900 K from a Machine-Learned Potential Trained with Diffusion Quantum Monte Carlo

Here, we survey the phase diagram of high-pressure molecular hydrogen with path integral molecular dynamics using a machine-learned interatomic potential trained with quantum Monte Carlo forces and energies. Besides the HCP and C2/c–24 phases, we find two new stable phases both with molecular centers in the Fmmm–4 structure, separated by a molecular orientation transition with temperature. The high temperature isotropic Fmmm–4 phase has a reentrant melting line with a maximum at higher temperature (1450 K at 150 GPa) than previously estimated and crosses the liquid-liquid transition line around 1200 K and 200 GPa.

08 HYDROGEN↗
DOE OSTI2022

Spin-orbital liquids and insulator-metal transitions on the pyrochlore lattice

The two orbital Hubbard model, with the electrons additionally coupled to a complex magnetic background, arises in the pyrochlore molybdates. The background involves local moments Hund's coupled to the electrons, driving double exchange ferromagnetism, and antiferromagnetic (AF) tendency arising from competing superexchange. The key scales include the Hubbard repulsion and the superexchange, both of which can be tuned in these materials. They control the phase transition from a ferromagnetic metal to a spin glass metal and then to a spin glass (Mott) insulator. We provide a comprehensive description of the ground state of this model using an unrestricted Hartree-Fock scheme implemented via a simulated annealing procedure and establish the metal-insulator transition line for varying Hubbard interaction and superexchange. The electrons see an effective disorder, due to orbital frustration, already in the ferromagnetic phase. The disorder is further enhanced by antiferromagnetic coupling and the resulting magnetic disorder. As a result, increasing AF coupling shifts the metal-insulator transition to lower Hubbard interaction and gives it an additional "Anderson" character. In conclusion, we provide detailed results on the magnetic and orbital correlations, the density of states, and the optical conductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Electronic excitation spectra of molecular hydrogen in phase I from quantum Monte Carlo and many-body perturbation methods

Here, we study the electronic excitation spectra in solid molecular hydrogen (phase I) at ambient temperature and 5- to 90-GPa pressures using quantum Monte Carlo methods and many-body perturbation theory. In this range, the system changes from a wide-gap molecular insulator to a semiconductor, altering the nature of the excitations from localized to delocalized. Computed gaps and spectra agree with experiments, proving the ability to predict accurately band gaps of many-body systems in the presence of nuclear quantum and thermal effects.

08 HYDROGEN↗
DOE OSTI2022

Matrix-Model Simulations Using Quantum Computing, Deep Learning, and Lattice Monte Carlo

Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes, and it underpins the only practical numerical approach to the study of complex high-dimensional supergravity theories. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount importance for the realization of a quantum theory of gravity. Moreover, a complete numerical understanding of the holographic duality and the emergence of geometric space-time features from microscopic degrees of freedom could pave the way for new discoveries in quantum information science. Euclidean lattice Monte Carlo simulations are the de facto numerical tool for understanding the spectrum of large matrix models and have been used to test the holographic duality. However, they are not tailored to extract dynamical properties or even the quantum wave function of the ground state of matrix models. Quantum computing and deep learning provide potentially useful approaches to study the dynamics of matrix quantum mechanics. If successful in the context of matrix models, these rapidly improving numerical techniques could become the new Swiss army knife of quantum gravity practitioners. In this paper, we perform the first systematic survey for quantum computing and deep-learning approaches to matrix quantum mechanics, comparing them to lattice Monte Carlo simulations. These provide baseline benchmarks before addressing more complicated problems. In particular, we test the performance of each method by calculating the low-energy spectrum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Dynamical exponent of a quantum critical itinerant ferromagnet: A Monte Carlo study

Here we consider the effect of the coupling between two-dimensional (2D) quantum rotors near an XY ferromagnetic quantum critical point and spins of itinerant fermions. We analyze how this coupling affects the dynamics of rotors and the self-energy of fermions. A common belief is that near a q = 0 ferromagnetic transition, fermions induce an Ω/q Landau damping of rotors (i.e., the dynamical critical exponent is z = 3) and Landau overdamped rotors give rise to non-Fermi liquid fermionic self-energy Σ∝ω 2/3 . This behavior has been confirmed in previous quantum Monte Carlo (QMC) studies. Here we show that for the XY case the behavior is different. We report the results of large-scale quantum Monte Carlo simulations, which show that at small frequencies z = 2 and Σ∝ω 1/2 . We argue that the new behavior is associated with the fact that a fermionic spin is by itself not a conserved quantity due to spin-spin coupling to rotors, and a combination of self-energy and vertex corrections replaces 1/q in the Landau damping by a constant. We discuss the implication of these results to experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Zero-point motion of liquid and solid hydrogen

We present an inelastic neutron scattering study of liquid and solid hydrogen carried out using the wide Angular Range Chopper Spectrometer at Oak Ridge National Laboratory. From the observed dynamic structure factor, we obtained empirical estimates of the molecular mean-squared displacement and average translational kinetic energy. Here we find that the former quantity increases with temperature, indicating that a combination of thermal and quantum effects is important near the liquid-solid phase transition, contrary to previous measurements. We also find that the kinetic energy drops dramatically on melting of the crystals, a consequence of the large increase in molar volume together with the Heisenberg indeterminacy principle. Our results are compared with quantum Monte Carlo simulations based on different model potentials. In general, there is good agreement between our findings and theoretical predictions based on the Silvera-Goldman and Buck potentials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization

We carry out extensive direct path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) at finite temperature for different values of the spin-polarization ξ. This allows us to unambiguously quantify the impact of spin effects on the momentum distribution function n(k) and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state n(0) substantially depend on ξ. Our results further advance the current understanding of the UEG as a fundamental model system, and are of practical relevance for the description of transport properties of warm dense matter in an external magnetic field. All PIMC results are freely available online and can be used as a benchmark for the development of methods and applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Lefschetz thimble quantum Monte Carlo for spin systems

Monte Carlo simulations are useful tools for modeling quantum systems, but in some cases they suffer from a sign problem, leading to an exponential slow down in their convergence to a value. While solving the sign problem is generically NP hard, many techniques exist for mitigating the sign problem in specific cases; in particular, the technique of deforming the Monte Carlo simulation's plane of integration onto Lefschetz thimbles (complex hypersurfaces of stationary phase) has seen significant success in the context of quantum field theories. We extend this methodology to spin systems by utilizing spin coherent state path integrals to reexpress the spin system's partition function in terms of continuous variables. Using some toy systems, we demonstrate its effectiveness at lessening the sign problem in this setting, despite the fact that the initial mapping to spin coherent states introduces its own sign problem. The standard formulation of the spin coherent path integral is known to make use of uncontrolled approximations; despite this, for large spins they are typically considered to yield accurate results, so it is somewhat surprising that our results show significant systematic errors. Furthermore, possibly of independent interest, our use of Lefschetz thimbles to overcome the intrinsic sign problem in spin coherent state path integral Monte Carlo enables a novel numerical demonstration of a breakdown in the spin coherent path integral.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Degeneracy engineering for classical and quantum annealing: A case study of sparse linear regression in collider physics

Classical and quantum annealing are computing paradigms that have been proposed to solve a wide range of optimization problems. In this paper, we aim to enhance the performance of annealing algorithms by introducing the technique of degeneracy engineering, through which the relative degeneracy of the ground state is increased by modifying a subset of terms in the objective Hamiltonian. We illustrate this novel approach by applying it to the example of ℓ 0 -norm regularization for sparse linear regression, which is, in general, an NP-hard optimization problem. Specifically, we show how to cast ℓ 0 -norm regularization as a quadratic unconstrained binary optimization (QUBO) problem, suitable for implementation on annealing platforms. As a case study, we apply this QUBO formulation to energy flow polynomials in high-energy collider physics, finding that degeneracy engineering substantially improves the annealing performance. Furthermore, our results motivate the application of degeneracy engineering to a variety of regularized optimization problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Absence of Off-Diagonal Long-Range Order in hcp 4 He Dislocation Cores

Here, the mass transport properties along dislocation cores in hcp 4 He are revisited by considering two types of edge dislocations as well as a screw dislocation, using a fully correlated quantum simulation approach. Specifically, we employ the zero-temperature path-integral ground state (PIGS) method together with ergodic sampling of the permutation space to investigate the fundamental dislocation core structures and their off-diagonal long-range order properties. It is found that the Bose-Einstein condensate fraction of such defective 4 He systems is practically null (≤ 10 –6 ), just as in the bulk defect-free crystal. These results provide compelling evidence for the absence of intrinsic superfluidity in dislocation cores in hcp 4 He and challenge the superfluid dislocation-network interpretation of the mass-flux-experiment observations, calling for further experimental investigation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Unified Approach to Polarons and Phonon-Induced Band Structure Renormalization

Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green’s function theory of band structure renormalization that incorporates localization and self-trapping. Here, we show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limit. To demonstrate this methodology, we reproduce the path-integral results of Feynman and diagrammatic Monte Carlo calculations for the Fröhlich model at all couplings, and we calculate the zero point renormalization of the band gap of an ionic insulator including polaronic effects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗