Session L25: Focus Session: Simulation of Matter at Extreme Conditions - Warm Dense Matter

Simulation of the Correlated Electron Plasma in the Warm Dense Matter Regime by Restricted Path-Integral Molecular Dynamics

Warm dense matter (WDM) can be characterized by electron temperatures of a few eV and densities an order of magnitude or more beyond ambient. This regime currently lacks any adequate highly developed class of simulation methods. Recent developments in orbital-free Density Functional Theory (ofDFT) aim to provide such a simulation method, however, little benchmark information is available on temperature and pressure dependence of simple but realistic models in WDM regime. The present work aims to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Within the discrete path integral representation, electrons are described as harmonic necklaces, while, quantum exchange takes the form of cross linking between electron necklaces. The fermion sign problem is addressed by restricting the density matrix to positive values and a molecular dynamics algorithm is employed to sample phase space. Here, we focus on the behavior of strongly correlated electron plasmas under WDM conditions. We compute the kinetic and potential energies and compare them to those obtained with the ofDFT method.   

Comparison of Finite Temperature Hartree-Fock and Density Functional Theory for Confined Systems

Warm dense matter (WDM) at elevated temperatures ({\it e.g.}, $T \approx 1$ to several eV) and densities ({\it e.g.} one or more orders of magnitude denser than equilibrium) is of growing importance. So far, the most detailed studies of WDM use Born-Oppenheimer molecular dynamics with ground-state density functional theory (DFT) approximations. Little, however, is known about the behavior of the free energy over the temperature and density ranges of interest. In the case of DFT, this deficiency is a barrier to assessing the validity of proposed approximate free-energy functionals. For insight into this problem, we have undertaken systematic numerical study of the thermal Hartree-Fock (THF) approximation. We report progress on application of THF to the problem of eight one-electron atoms at arbitrary positions in a hard-walled box. We discuss the physics which emerges for both high- and low-symmetry ionic arrays, including molecular binding transitions. In addition, we compare the THF results directly with approximate DFT results, including approximate finite-temperature orbital-free kinetic and exchange functionals.   

The Korringa-Kohn-Rostoker Method Applied to Warm Dense Matter

The electronic structure, EOS and transport properties of warm electrons in an amorphous or disordered configuration of ions is not well described by either solid-state or plasma models. Such warm, dense systems share the characteristic of the solid state that multi-center scattering effects are of paramount importance in forming bands of valence states. Theoretical treatment of the EOS of warm, dense matter therefore requires a way to include significant occupation of higher energy and angular momentum channel continuum states. We are extending the Green's function Kohn-Korringa-Rostoker code \emph{MECCA} as an all-electron (non-pseudo potential) method that treats arbitrary mixtures of atoms on an ab-initio basis over a broad range of conditions, from cold, solid matter up to hot plasmas at extreme (ICF) compression. Specific examples of Aluminum and Boron-Nitride will be discussed.   

Density Functional versus Thermal Hartree-Fock Approximations in Warm Dense Lithium

We compare the behaviors of the thermal Hartree-Fock (tHF) model and thermal Density Functional Theory (tDFT) using both ground-state and temperature-dependent approximate functionals. The test system is bcc Li in the temperature-density regime of warm dense matter. In the exchange-only case, we find significant qualitative differences between the exact tHF and the DFT calculations with zero-temperature local density approximation (LDA) exchange. A temperature-dependent LDA functional provides much better agreement with the tHF exchange. An underlying need is for well-characterized, reliable pseudopotentials over demanding temperature and density ranges. Thus we compare pseudopotential and all-electron results for small Li clusters of local bcc symmetry and bond-lengths appropriate to high density bulk Li. We determine the density range over which both standard projector-augmented wave(PAW) and norm-conserving pseudopotentials are reliable. Then we construct small-cutoff-radius PAW data sets (for both the local density and the generalized gradient exchange-correlation approximations) which are valid for lithium densities up to at least 80 g/cm$^3$.   

A Different Time-Dependent Variational Principle Approach: Going Beyond Wave Packet Molecular Dynamics

During inertial confinement fusion, matter evolves from a solid condensed matter phase through the warm dense matter (WDM) regime to a hot dense matter. In WDM, quantum mechanical effects are important because of both Fermi-Dirac statistics and the rate of electrons transitioning in and out of bound states is large. The time-dependent temperature and quickly changing local environment require a time-dependent quantum method. A converged dynamical quantum simulation is intractable for more than a few particles. Instead, we take as a feasible goal to match the statistical properties of a warm dense plasma. The time-dependent variational principle gives a framework for producing equations of motion. A commonly used variational form is a Hartree product of isotropic Gaussian wave packets (wave packet molecular dynamics). The resulting dynamics do not produce the right statistics. We therefore introduce a plane wave basis and discuss its advantages and test its ability to reproduce radial distribution functions produced by hyper-netted chain calculations.   

All-Electron Path Integral Simulations of Warm, Dense Matter: Application to Water and Carbon

We develop an all-electron path integral Monte Carlo (PIMC) method for warm dense matter and apply it to study water and carbon. PIMC pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics (DFT-MD) at lower temperatures and enable the construction of a coherent equation of state over a density-temperature range of 3--12 g/cm$^3$ and 10$^2$--10$^9$ K. PIMC results converge to the Debye-Huckel limiting law at high-temperatures and illuminate the breakdown of DFT pseudopotentials due to core excitations.   

Non-equilibrium Warm Dense Matter: Electron-Ion Dynamics of Pumped Nanofoils

In 2006, it was reported that the dielectric function of laser-excited gold nanofoils exhibits a peculiar behavior; the interband transition peak of gold is enhanced and undergoes a clear red shift [PRL \textbf{96}, 255003 (2006)]. In 2009, based on ultrafast electron diffraction measurements on pumped gold nanofoils, it was reported that the time evolution of the Debye-Waller factor is too slow to be explained by a two-temperature model that included temperature dependent el-ph coupling. This anomaly has been attributed to a phonon hardening process caused by high electron temperatures (a few eV) [Science \textbf{323}, 1033 (2009)]. Later, it was pointed out that at such a high electron temperatures the dielectric function of gold calculated by first-principles DFT simulations does not reproduce the enhanced and red-shifted interband transition peak and an alternative explanation was proposed to reconcile the discrepancies where the effect of ejected electrons was addressed [HEDP \textbf{6}, 246 (2010)]. In this talk, we will discuss recent experimental/theoretical efforts to further examine the issues relevant to this problem, el-ph coupling, dynamics of ejected electrons, and ballistic transport of electrons [submitted to HEDP; PRL \textbf{106}, 167601(2011)].   

High field terahertz response of materials

We report on studies of the response of materials to intense ultrashort electromagnetic fields at terahertz frequencies. These are generated through coherent transition radiation using femtosecond electron bunches at the Linac Coherent Light Source and correspond to single-cycle pulses with electric field amplitudes > 20 MV/cm with a frequency centered at ~10 THz. Large amplitude nonlinear responses are observed in a range of semiconductor materials associated with field-induced ionization processes, and we show how these processes can be used to carry out nonlinear autocorrelation measurements of the pulse shape. We also discuss recent results probing the response of ferroelectric materials at high fields coupled with ultrafast x-ray probes enabling measurement of their atomic-scale response on sub-picosecond time-scales.   

An Analytic Screening Potential for Dense, Strongly-Coupled Plasmas

Characterizing warm dense matter (WDM) has gained renewed interest due to advances in powerful lasers and next generation light sources. Because WDM is strongly coupled and moderately degenerate, we must often rely on simulations of WDM, which are necessarily based on molecular dynamics of ions interacting through a screened potential. Almost always, a Debye- (Yukawa-) like interaction is assumed; however, it is well known that such long wavelength models over-screen. Here, we present a new effective ion-ion interaction, which recovers the exact fermionic linear response in the long-wave limit while retaining a pair-potential functionally similar to that of the Yukawa form. This new potential not only improves the accuracy of screening effects without contributing to the computational complexity of the model, but it also adds physics entirely missing from Yukawa models (such as the onset of Friedel oscillations). Simulations of the ion structure factor are compared to XRTS data for Be and C in the WDM regime.   

Large-Scale Reactive Simulations of Materials in Extreme Conditions

First-principles quantum mechanics methods are inadequate for accurately describing the effects of thermal, mechanical, chemical or radiation excitations that may occur in materials operating under extreme conditions, or impractical to use due to the prohibitive scaling cost of propagating the total Schrodinger equation for a large set of atoms. In the regime of a high number of electronic excitations, the electronic portion of the wave function contains contributions from many stationary states, and the Born-Oppenheimer approximation breaks down. We have been developing a mixed quantum-classical dynamics approach, called the Electron Force Field (eFF), to simulate the non-adiabatic dynamics of materials in extreme conditions. We have demonstrated its application to describe the: thermodynamics of dense hydrogen over 0-100,000 Kelvin; real-time dynamics of Auger fragmentation of diamond nano particles; transient electronic effects in high-strain rate silicon fracture; Coulomb explosion of carbon clusters; dynamics of cascaded valence ionizations in shocked hydrocarbons; and the dynamics of hypervelocity impact of materials. Here, we summarize our recent progress in the theory and application of eFF for modeling and simulation of materials in extreme conditions.   

First-principle Calculations of Equation of State for Metals at High Energy Density

In this work, we present quantum molecular dynamics calculations of the shock Hugoniots of solid and porous samples as well as release isentropes and isentropic sound velocity behind the shock front for aluminum. Also we perform similar calculations for nickel and iron. We use the VASP code with ultrasoft and PAW pseudopotentials and GGA exchange-correlation functional. Up to 512 particles have been used in calculations. To calculate Hugoniots we solve the Hugoniot equation numerically. To obtain release isentropes, we use Zel'dovich's approach and integrate an ordinary differential equation for the temperature thus restoring all thermodynamic parameters. Isentropic sound velocity is calculated by differentiation of pressure along isentropes. The results of our calculations are in good agreement with experimental data at densities both higher and lower than the normal one. Thus, quantum molecular dynamics results can be effectively used for verification or calibration of semiempirical equations of state under conditions of lack of experimental information at high energy densities.   

Color quantum simulations of strongly coupled quark-gluon plasma

We propose stochastic simulation of thermodynamics and kinetic properties for quark-gluon plasma (QGP) in semi-classical approximation in the wide region of temperature, density and quasi-particles masses. In grand canonical ensemble for finite and zero baryon chemical potential we use the direct quantum path integral Monte Carlo method (PIMC) developed for finite temperature within Feynman formulation of quantum mechanics to do calculations of internal energy, pressure and pair correlation functions. The QGP quasi-particles representing dressed quarks, antiquarks and gluons interact via color quantum Kelbg pseudopotential rigorously derived for Coulomb particles. This method has been successfully applied to strongly coupled electrodynamic plasmas (EMP). A strongly correlated behavior of the QGP is expected to show up in long-ranged spatial correlations of quarks and gluons which, in fact, may give rise to liquid-like and, possibly, solid-like structures. We have done already the first calculation of the QGP equation of state, spatial and color pair distribution functions, diffusion coefficients and shear viscosity.   

Proton crystallization and quantum melting of proton crystals in a dense hydrogen plasma

We present extensive new simulation results which allow to predict the temperature and density range for proton crystallization. We simulate a macroscopic spatially homogeneous fully ionized two-component electron-proton plasma in thermodynamic equilibrium from first principles using direct fermionic path integral Monte Carlo simulations. Our results for the phase diagram differ substantially from the previous predictions based on the one-component plasma (OCP) model: In the classical part of the phase diagram the crystal appears to be stabilized compared to the OCP predition. In contrast, in the quantum part of the phase diagram the crystal appears to be de-stabilized and vanishes at lower densities compared to the OCP prediction. Finally, the maximum temperature for the proton crystal is found to be around 40 000K, slightly below the previous prediction. Our results indicate that the OCP treatment of the liquid-solid transition in a two-component plasma has to be questioned. The OCP-assumption of a homogeneous rigid neutralizing background gives rise to substantial deviations of the critical parameters.