We simulate high-pressure hydrogen in its liquid phase close to molecular dissociation using a machine-learned interatomic potential. The model is trained with density functional theory forces and energies, with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. We show that an accurate NequIP model, an E(3)-equivariant neural network potential, accurately reproduces the phase transition present in PBE. Moreover, the computational efficiency of this model allows for substantially longer molecular-dynamics trajectories, enabling us to perform a finite-size scaling analysis to distinguish between a crossover and a true first-order phase transition. We locate the critical point of this transition, the liquid-liquid phase transition, at 1200-1300 K and 155-160 GPa, a temperature lower than most previous estimates and close to the melting transition.

We present results and discuss methods for computing the melting temperature of dense molecular hydrogen using a machine learned model trained on quantum Monte Carlo data. In this newly trained model, we emphasize the importance of accurate total energies in the training. We integrate a two phase method for estimating the melting temperature with estimates from the Clausius-Clapeyron relation to provide a more accurate melting curve from the model. We make detailed predictions of the melting temperature, solid and liquid volumes, latent heat and internal energy from 50 GPa to 180 GPa for both classical hydrogen and quantum hydrogen. At pressures of roughly 173 GPa and 1635K, we observe molecular dissociation in the liquid phase. We compare with previous simulations and experimental measurements.

We calculate the melting lines 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. 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.

Quantum Monte Carlo (QMC) can play a very important role in generating accurate data needed for constructing potential energy surfaces. We argue that QMC has advantages in terms of a smaller systematic bias and an ability to cover phase space more completely. The stochastic noise can ease the training of the machine learning model. We discuss how stochastic errors affect the generation of effective models by analyzing the errors within a linear least squares procedure, finding that there is an advantage to having many relatively imprecise data points for constructing models. We then analyze the effect of noise on a model of many-body silicon finding that noise in some situations improves the resulting model. We then study the effect of QMC noise on two machine learning models of dense hydrogen used in a recent study of its phase diagram. The noise enable us to estimate the errors in the model. We conclude with a discussion of future research problems.

Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g., planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement fusion. There exists experimental data for the equation of state, conductivity, and Thomson scattering spectra. However, the analysis of the measurements at extreme pressures and temperatures typically involves additional model assumptions, which makes it difficult to assess the accuracy of the experimental data rigorously. On the other hand, theory and modeling have produced extensive collections of data. They originate from a very large variety of models and simulations including path integral Monte Carlo (PIMC) simulations, density functional theory (DFT), chemical models, machine-learned models, and combinations thereof. At the same time, each of these methods has fundamental limitations (fermion sign problem in PIMC, approximate exchange–correlation functionals of DFT, inconsistent interaction energy contributions in chemical models, etc.), so for some parameter ranges accurate predictions are difficult. Recently, a number of breakthroughs in first principles PIMC as well as in DFT simulations were achieved which are discussed in this review. Here we use these results to benchmark different simulation methods. We present an update of the hydrogen phase diagram at high pressures, the expected phase transitions, and thermodynamic properties including the equation of state and momentum distribution. Furthermore, we discuss available dynamic results for warm dense hydrogen, including the conductivity, dynamic structure factor, plasmon dispersion, imaginary-time structure, and density response functions. We conclude by outlining strategies to combine different simulations to achieve accurate theoretical predictions that are based on first principles.

We study the electronic excitation spectra in solid molecular hydrogen (phase I) at ambient temperature and 5-90 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 presence of nuclear quantum and thermal effects.

Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g. planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement fusion. There exists experimental data for the equation of state, conductivity, and Thomson scattering spectra. However, the analysis of the measurements at extreme pressures and temperatures typically involves additional model assumptions, which makes it difficult to assess the accuracy of the experimental data. rigorously. On the other hand, theory and modeling have produced extensive collections of data. They originate from a very large variety of models and simulations including path integral Monte Carlo (PIMC) simulations, density functional theory (DFT), chemical models, machine-learned models, and combinations thereof. At the same time, each of these methods has fundamental limitations (fermion sign problem in PIMC, approximate exchange-correlation functionals of DFT, inconsistent interaction energy contributions in chemical models, etc.), so for some parameter ranges accurate predictions are difficult. Recently, a number of breakthroughs in first principle PIMC and DFT simulations were achieved which are discussed in this review. Here we use these results to benchmark different simulation methods. We present an update of the hydrogen phase diagram at high pressures, the expected phase transitions, and thermodynamic properties including the equation of state and momentum distribution. Furthermore, we discuss available dynamic results for warm dense hydrogen, including the conductivity, dynamic structure factor, plasmon dispersion, imaginary-time structure, and density response functions. We conclude by outlining strategies to combine different simulations to achieve accurate theoretical predictions.

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. 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.

We discuss the methodology of quantum Monte Carlo calculations of the effective mass based on the static self-energy Σ(k,0). We then use variational Monte Carlo calculations of Σ(k,0) of the homogeneous electron gas at various densities to obtain results very close to perturbative G_{0}W_{0} calculations for values of the density parameter 1≤r_{s}≤10. The obtained values for the effective mass are close to diagrammatic Monte Carlo results and disagree with previous quantum Monte Carlo calculations based on a heuristic mapping of excitation energies to those of an ideal gas.

hydrogen-rich compound has taken the lead in the race for a material that can conduct electricity with zero resistance at room temperature and ambient pressure — the conditions required for many technological applications.

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 (1450K at 150GPa) than previously estimated and crosses the liquid-liquid transition line around 1200K and 200GPa.

We present a method of calculating the energy gap of a charge-neutral excitation using only ground-state calculations. We report Quantum Monte Carlo calculations of Γ→ Γ and Γ → X particle-hole excitation energies in diamond carbon. We analyze the finite-size effect and find the same 1/L decay rate as that in a charged excitation, where L is the linear extension of the supercell. This slow decay is attributed to the delocalized nature of the excitation in supercells too small to accommodate excitonic binding effects. At larger system sizes, the apparent 1/L decay crosses over to a 1/L3 behavior. Estimation of the scale of exciton binding can be used to correct finite-size effects of neutral gaps.

We describe a simple scheme to perform phonon calculations with quantum Monte Carlo (QMC) methods and demonstrate it on metallic hydrogen. Because of the energy and length scales of metallic hydrogen and the statistical noise inherent to QMC methods, the conventional manner of calculating force constants is prohibitively expensive. We show that our alternate approach is nearly 100 times more efficient in resolving the force constants needed to calculate the phonon spectrum in the harmonic approximation. This requires only the calculation of atomic forces, as in the conventional approach, and otherwise little or no programmatic modification.

The synthesis of the high temperature superconductor LaH10 requires pressures in excess of 100 GPa, wherein it adopts a face-centered cubic structure. Upon decompression, this structure undergoes a distortion which still supports superconductivity, but with a much lower critical temperature. Previous calculations have shown that quantum and anharmonic effects are necessary to stabilize the cubic structure, but have not resolved the low pressure distortion. Using large scale path-integral molecular dynamics enabled by a machine learned potential, we show that a rhombohedral distortion appears at sufficiently low pressures, even with quantum and anharmonic effects. We also highlight the importance of quantum zero point motion in stabilizing the cubic structure.

Structures from the Stone Age can provide unique insights into Late Glacial and Mesolithic cultures around the Baltic Sea. Such structures, however, usually did not survive within the densely populated Central European subcontinent. Here, we ...The Baltic Sea basins, some of which only submerged in the mid-Holocene, preserve Stone Age structures that did not survive on land. Yet, the discovery of these features is challenging and requires cross-disciplinary approaches between archeology and ...

Received 18 March 2021DOI:https://doi.org/10.1103/PhysRevX.11.029901Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.© 2021 American Physical SocietyPhysics Subject Headings (PhySH)Physical Systems1-dimensional systemsStrongly correlated systemsTechniquesElectronic structureFirst-principles calculationsNumerical techniquesQuantum chemistry methodsCondensed Matter & Materials Physics

We computed the Compton profile of solid and liquid lithium using quantum Monte Carlo (QMC) and compared with recent experimental measurements obtaining good agreement. Importantly, we find it crucial to account for proper core-valence orthogonalization and to address density differences when comparing with experiment. To account for disorder effects, we sampled finite-temperature configurations using molecular dynamics (MD), then performed diffusion Monte Carlo (DMC) simulations on each configuration. We used Slater-Jastrow wavefunctions and grand-canonical twist-averaged boundary conditions. A QMC pseudopotential correction, derived from an all-electron DMC simulation of the perfect crystal was also used. Our calculations provide the first all-electron QMC benchmark for the Compton profile of lithium crystal and pseudopotential-corrected QMC Compton profiles for both the liquid and solid.