Coupled Electron Ion Monte Carlo Calculations of Dense Metallic Hydrogen

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

Metropolis Methods for Quantum Monte Carlo Simulations

Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of the Metropolis algorithm employed in quantum Monte Carlo: Variational Monte Carlo, dynamical methods for projector monte carlo ({\it i.e.} diffusion Monte Carlo with rejection), multilevel sampling in path integral Monte Carlo, the sampling of permutations, cluster methods for lattice models, the penalty method for coupled electron-ionic systems and the Bayesian analysis of imaginary time correlation functions.Comment: Proceedings of "Monte Carlo Methods in the Physical Sciences" Celebrating the 50th Anniversary of the Metropolis Algorith

Quantum Monte Carlo Simulation of the High-Pressure Molecular-Atomic Crossover in Fluid Hydrogen

A first-order liquid-liquid phase transition in high-pressure hydrogen between molecular and atomic fluid phases has been predicted in computer simulations using ab initio molecular dynamics approaches. However, experiments indicate that molecular dissociation may occur through a continuous crossover rather than a first-order transition. Here we study the nature of molecular dissociation in fluid hydrogen using an alternative simulation technique in which electronic correlation is computed within quantum Monte Carlo, the so-called Coupled Electron Ion Monte Carlo (CEIMC) method. We find no evidence for a first-order liquid-liquid phase transition.Comment: 4 pages, 5 figures; content changed; accepted for publication in Phys. Rev. Let

Path Integral Monte Carlo Simulations for Fermion Systems: Pairing in the Electron-Hole Plasma

We review the path integral method wherein quantum systems are mapped with Feynman's path integrals onto a classical system of "ring-polymers" and then simulated with the Monte Carlo technique. Bose or Fermi statistics correspond to possible "cross-linking" of polymers. As proposed by Feynman, superfluidity and Bose condensation result from macroscopic exchange of bosons. To map fermions onto a positive probability distribution, one must restrict the paths to lie in regions where the fermion density matrix is positive. We discuss a recent application to the two-component electron-hole plasma. At low temperature excitons and bi-excitons form. We have used nodal surfaces incorporating paired fermions and see evidence of a Bose condensation in the energy, specific heat and superfluid density. In the restricted path integral picture, pairing appears as intertwined electron-hole paths. Bose condensation occurs when these intertwined paths wind around the periodic boundaries.Comment: 14 pages, 7 figures Prepared for the 1999 International Conference on Strongly Coupled Coulomb Systems, Saint-Malo, Franc

Lowering of the Kinetic Energy in Interacting Quantum Systems

Interactions never lower the ground state kinetic energy of a quantum system. However, at nonzero temperature, where the system occupies a thermal distribution of states, interactions can reduce the kinetic energy below the noninteracting value. This can be demonstrated from a first order weak coupling expansion. Simulations (both variational and restricted path integral Monte Carlo) of the electron gas model and dense hydrogen confirm this and show that in contrast to the ground state case, at nonzero temperature the population of low momentum states can be increased relative to the free Fermi distribution. This effect is not seen in simulations of liquid He-3.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett., June, 200

Equation of state of metallic hydrogen from Coupled Electron-Ion Monte Carlo simulations

We present a study of hydrogen at pressures higher than molecular dissociation using the Coupled Electron-Ion Monte Carlo method. These calculations use the accurate Reptation Quantum Monte Carlo method to estimate the electronic energy and pressure while doing a Monte Carlo simulation of the protons. In addition to presenting simulation results for the equation of state over a large region of phase space, we report the free energy obtained by thermodynamic integration. We find very good agreement with DFT calculations for pressures beyond 600 GPa and densities above $\rho=1.4 g/cm^3$. Both thermodynamic as well as structural properties are accurately reproduced by DFT calculations. This agreement gives a strong support to the different approximations employed in DFT, specifically the approximate exchange-correlation potential and the use of pseudopotentials for the range of densities considered. We find disagreement with chemical models, which suggests a reinvestigation of planetary models, previously constructed using the Saumon-Chabrier-Van Horn equations of state.Comment: 9 pages, 7 figure

The Coupled Electronic-Ionic Monte Carlo Simulation Method

Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion Monte Carlo or Path Integral Monte Carlo are the most accurate and general methods for computing total electronic energies. We will review methods we have developed to perform QMC for the electrons coupled to a classical Monte Carlo simulation of the ions. In this method, one estimates the Born-Oppenheimer energy E(Z) where Z represents the ionic degrees of freedom. That estimate of the energy is used in a Metropolis simulation of the ionic degrees of freedom. Important aspects of this method are how to deal with the noise, which QMC method and which trial function to use, how to deal with generalized boundary conditions on the wave function so as to reduce the finite size effects. We discuss some advantages of the CEIMC method concerning how the quantum effects of the ionic degrees of freedom can be included and how the boundary conditions can be integrated over. Using these methods, we have performed simulations of liquid H2 and metallic H on a parallel computer.Comment: 27 pages, 10 figure