We present a new Monte Carlo method which couples Path Integral for finite temperature protons with Quantum Monte Carlo for ground state electrons, and we apply it to metallic hydrogen for pressures beyond molecular dissociation. We report data for the equation of state for temperatures across the melting of the proton crystal. Our data exhibit more structure and higher melting temperatures of the proton crystal than Car-Parrinello Molecular Dynamics results. This method fills the gap between high temperature electron-proton Path Integral and ground state Diffusion Monte Carlo methods.
Many body trial wave functions are the key ingredient for accurate Quantum Monte Carlo estimates of total electronic energies in many electron systems. In the Coupled Electron-Ion Monte Carlo method, the accuracy of the trial function must be conjugated with the efficiency of its evaluation. We report recent progress in trial wave functions for metallic hydrogen implemented in the Coupled Electron-Ion Monte Carlo method. We describe and characterize several types of trial functions of increasing complexity in the range of the coupling parameter $1.0 \leq r_s \leq1.55$. We report wave function …
Liquid-liquid phase transition of hydrogen is at the center of hydrogen phase diagram as a promising route towards emergent properties such as the Wigner-Huntington metallization, superconductivity, and superfluidity. Here we report a study on the liquid-liquid phase transition of hydrogen using the state-of-the-art diffusion quantum Monte Carlo and density functional theory calculations. Our results suggest that the metallization process happens at lower pressures and temperatures compared to the structural phase transition of molecular to atomic hydrogen. The consequence is that metallized m…
Ab initio random structure searching with density functional theory was used to determine the zero-temperature structures of atomic metallic hydrogen from 500 GPa to 5 TPa. Including zero point motion in the harmonic approximation, we estimate that molecular hydrogen dissociates into a monatomic body-centered tetragonal structure near 500 GPa (r_s = 1.225), which then remains stable to 2.5 TPa (r_s = 0.969). At higher pressures, hydrogen stabilizes in an ...ABCABC... planar structure that is remarkably similar to the ground state of lithium, which compresses to the face-centered cubic lattice …
Superconductivity in the recently proposed ground-state structures of atomic metallic hydrogen is investigated over the pressure range 500 GPa to 3.5 TPa. Near molecular dissociation, the electron--phonon coupling $λ$ and renormalized Coulomb repulsion are similar to the molecular phase. A continuous increase in the critical temperature $T_c$ with pressure is therefore expected, to $\jmmapprox 356$K near 500 GPa. As the atomic phase stabilizes with increasing pressure, $λ$ increases, causing $T_c$ to approach $\jmmapprox 481$K near 700 GPa. At the first atomic--atomic structural phase transfor…
Ab initio molecular dynamic method within the framework of density functional theory is applied to analyze the structural and electronic properties of crystalline molecular hydrogen at temperature 100\,K. Pressure, pair correlation function and band structure are calculated. The crossover of molecular crystalline hydrogen from the state of a semiconductor to a semimetallic and metallic state is observed upon compression in the pressure range of 302-626\,GPa. At pressures below 361\,GPa, the molecular crystal with the C2/c structure is a semiconductor with an indirect gap. In the pressure range…
Superatomic hydrogen: achieving effective aggregation of hydrogen atoms at pressures lower than that of metallic hydrogen
Institute of Atomic and Molecular Physics, Jilin University（吉林大学原子与分子物理研究所）；Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University（吉林大学物理学院教育部材料模拟方法与技术重点实验室）；Institute of Theoretical Chemistry, College of Chemistry, Jilin University（吉林大学化学学院理论化学研究所）
A new variational principle for optimizing thermal density matrices is introduced. As a first application, the variational many body density matrix is written as a determinant of one body density matrices, which are approximated by Gaussians with the mean, width and amplitude as variational parameters. The method is illustrated for the particle in an external field problem, the hydrogen molecule and dense hydrogen where the molecular, the dissociated and the plasma regime are described. Structural and thermodynamic properties (energy, equation of state and shock Hugoniot) are presented.
The temperature-dependent effective potential (TDEP) method for anharmonic phonon dispersion is generalized to the full potential case by combining with path integral formalism. This extension naturally resolves the intrinsic difficulty in the original TDEP at low temperature. The new method is applied to solid metallic hydrogen at high pressure. A colossal nuclear quantum effect (NQE) and subsequent anharmonicity are discovered, which not only leads to unexpectedly large drift of protons, but also slows down the convergence rate substantially when computing the phonon dispersions. By employin…
For a long time, there have been huge discrepancies between different models and experiments concerning the liquid-liquid phase transition (LLPT) in dense hydrogen. In this work, we present the results of extensive calculations of the LLPT in dense hydrogen using the most expensive first-principle path-integral molecular dynamics simulations available. The nonlocal density functional rVV10 and hybrid functional PBE0 are used to improve the description of the electronic structure of hydrogen. Of all the density functional theory calculations available, we report the most consistent results thro…
The properties of hydrogen under extreme conditions are important for many applications, including inertial confinement fusion and astrophysical models. A key quantity is given by the electronic density response to an external perturbation, which is probed in X-ray Thomson scattering (XRTS) experiments -- the state of the art diagnostics from which system parameters like the free electron density $n_e$, the electronic temperature $T_e$, and the charge state $Z$ can be inferred. In this work, we present highly accurate path integral Monte Carlo (PIMC) results for the electronic density response…
Deep Variational Free Energy Approach to Dense Hydrogen
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Institute of Applied Physics and Computational Mathematics（北京应用物理与计算数学研究所）；DP Technology（深势科技）；AI for Science Institute（科学智能研究院）；Songshan Lake Materials Laboratory（松山湖材料实验室）
Using Quantum Monte Carlo (QMC) calculations, we investigate the insulator-metal transition observed in liquid hydrogen at high pressure. Below the critical temperature of the transition from the molecular to the atomic liquid, the fundamental electronic gap closure occurs abruptly, with a small discontinuity reflecting the weak first-order transition in the thermodynamic equation of state. Above the critical temperature, molecular dissociation sets in while the gap is still open. When the gap closes, the decay of the off-diagonal reduced density matrix shows that the liquid enters a gapless, …
The Kubo-Greenwood (KG) formula is often used in conjunction with Kohn-Sham (KS) density functional theory (DFT) to compute the optical conductivity, particularly for warm dense mater. For applying the KG formula, all KS eigenstates and eigenvalues up to an energy cutoff are required and thus the approach becomes expensive, especially for high temperatures and large systems, scaling cubically with both system size and temperature. Here, we develop an approach to calculate the KS conductivity within the stochastic DFT (sDFT) framework, which requires knowledge only of the KS Hamiltonian but not…
Solid rigidity and liquid-scale mobility are thought incompatible in elemental substances. One cannot have an elemental solid that is long-range positionally ordered wherein the atoms flow like in a liquid simultaneously. The only exception might be the hypothetical supersolid state of 4He. In this work, we demonstrate that such exotic state could exist even in the classical regime. Using ab initio molecular dynamics (AIMD) and ab initio path integral molecular dynamics (AI-PIMD), a novel state of dense hydrogen which simultaneously has both long-range spatial ordering and liquid-scale atomic …
Lattice stability and metastability, as well as melting, are important features of the physics and chemistry of dense hydrogen. Using ab initio molecular dynamics (AIMD), the classical superheating limit and melting line of metallic hydrogen are investigated up to 1.5 TPa. The computations show that the classical superheating degree is about 100 K, and the classical melting curve becomes flat at a level of 350 K when beyond 500 GPa. This information allows us to estimate the well depth and the potential barriers that must be overcome when the crystal melts. Inclusion of nuclear quantum effects…
Structural behavior and equation of state of atomic and molecular crystal phases of dense hydrogen at pressures up to 3.5 TPa are systematically investigated with density functional theory. The results indicate that the Vinet EOS model that fitted to low-pressure experimental data overestimates the compressibility of dense hydrogen drastically when beyond 500 GPa. Metastable multi-atomic molecular phases with weak covalent bonds are observed. When compressed beyond about 2.8 TPa, these exotic low-coordinated phases become competitive with the groundstate and other high-symmetry atomic phases. …
We propose an ab-initio molecular dynamics method, capable to reduce dramatically the autocorrelation time required for the simulation of classical and quantum particles at finite temperature. The method is based on an efficient implementation of a first order Langevin dynamics modified by means of a suitable, position dependent acceleration matrix $S$. Here we apply this technique, within a Quantum Monte Carlo (QMC) based wavefuntion approach and within the Born-Oppheneimer approximation, for determining the phase diagram of high-pressure Hydrogen with simulations much longer than the autocor…
