The package "fhi96md" is an efficient code to perform density-functional theory total-energy calculations for materials ranging from insulators to transition metals. The package employs first-principles pseudopotentials, and a plane-wave basis-set. For exchange and correlation both the local density and generalized gradient approximations are implemented. The code has a low storage demand and performs efficiently on low budget personal computers as well as high performance computers.

Density-functional theory calculations for poly-atomic systems: Electronic structure, static and elastic properties and ab initio molecular dynamics

The uniform electron gas at warm dense matter conditions

We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space many-body systems. The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much greater size than that accessible to conventional PIMC simulations. As an illustrative application of the method, we simulate the superfluid transition of 4He in two dimensions.

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Worm algorithm for continuous-space Path Integral Monte Carlo simulations

In a recent Letter [T. Dornheim et al., Phys. Rev. Lett. 117, 156403 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.156403], we presented the first quantum Monte Carlo (QMC) results for the warm dense electron gas in the thermodynamic limit. However, a complete parametrization of the exchange-correlation free energy with respect to density, temperature, and spin polarization remained out of reach due to the absence of (i) accurate QMC results below θ=k_{B}T/E_{F}=0.5 and (ii) QMC results for spin polarizations different from the paramagnetic case. Here we overcome both remaining limitations. By closing the gap to the ground state and by performing extensive QMC simulations for different spin polarizations, we are able to obtain the first completely ab initio exchange-correlation free energy functional; the accuracy achieved is an unprecedented ∼0.3%. This also allows us to quantify the accuracy and systematic errors of various previous approximate functionals.

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Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions.

We perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with the linear response theory, we are able to remove finite-size errors from the potential energy over the substantial parts of the warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)]. Extensive new QMC results for up to $N=1000$ electrons enable us to compute the potential energy $V$ and the exchange-correlation free energy ${F}_{\mathrm{xc}}$ of the macroscopic electron gas with an unprecedented accuracy of $|\mathrm{\ensuremath{\Delta}}V|/|V|,|\mathrm{\ensuremath{\Delta}}{F}_{\mathrm{xc}}|/|F{|}_{\mathrm{xc}}\ensuremath{\sim}{10}^{\ensuremath{-}3}$. A comparison of our new data to the recent parametrization of ${F}_{\mathrm{xc}}$ by Karasiev et al. [Phys. Rev. Lett. 112, 076403 (2014)] reveals significant deviations to the latter.

/pdf/ab-initio-quantum-monte-carlo-simulation-of-the-warm-dense-40692w96lf.pdf

Ab Initio Quantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

The uniform electron gas at finite temperature is of key relevance for many applications in dense plasmas, warm dense matter, laser excited solids, and much more. Accurate thermodynamic data for the uniform electron gas are an essential ingredient for many-body theories, in particular, density-functional theory. Recently, first-principles restricted path integral Monte Carlo results became available, which, however, had to be restricted to moderate degeneracy, i.e., low to moderate densities with r_{s}=r[over ¯]/a_{B}≳1. Here we present novel first-principles configuration path integral Monte Carlo results for electrons for r_{s}≤4. We also present quantum statistical data within the e^{4} approximation that are in good agreement with the simulations at small to moderate r_{s}.

/pdf/ab-initio-thermodynamic-results-for-the-degenerate-electron-2ip5gcilby.pdf

Ab Initio Thermodynamic Results for the Degenerate Electron Gas at Finite Temperature.

A novel path integral Monte Carlo (PIMC) approach for correlated many-particle systems with arbitrary pair interaction in continuous space at low temperatures is presented. It is based on a representation of the N -particle density operator in a basis of (anti-)symmetrized N -particle states (configurations of occupation numbers). The path integral is transformed into a sum over trajectories with the same topology and, finally, the limit of M ∞, where M is the number of high-temperature factors, is analytically performed. This yields exact expressions for the thermodynamic quantities and allows to perform efficient simulations for fermions at low temperature and weak to moderate coupling. Our method is expected to be applicable to dense quantum plasmas in the regime of strong degeneracy where conventional PIMC fails due to the fermion sign problem (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Configuration Path Integral Monte Carlo

The effective potential Φ of a classical ion in a weakly correlated quantum plasma in thermodynamic equilibrium at finite temperature is well described by the random phase approximation screened Coulomb potential. Additionally, collision effects can be included via a relaxation time ansatz (Mermin dielectric function). These potentials are used to study the quality of various statically screened potentials that were recently proposed by Shukla and Eliasson (SE) [Phys. Rev. Lett. 108, 165007 (2012)], Akbari-Moghanjoughi (AM) [Phys. Plasmas 22, 022103 (2015)], and Stanton and Murillo (SM) [Phys. Rev. E 91, 033104 (2015)] starting from quantum hydrodynamic (QHD) theory. Our analysis reveals that the SE potential is qualitatively different from the full potential, whereas the SM potential (at any temperature) and the AM potential (at zero temperature) are significantly more accurate. This confirms the correctness of the recently derived [Michta et al., Contrib. Plasma Phys. 55, 437 (2015)] pre-factor 1/9 in front of the Bohm term of QHD for fermions.

/pdf/statically-screened-ion-potential-and-bohm-potential-in-a-5d39587tha.pdf

Statically screened ion potential and Bohm potential in a quantum plasma

Warm dense matter is one of the most active frontiers in plasma physics due to its relevance for dense astrophysical objects and for novel laboratory experiments in which matter is being strongly compressed, e.g., by high-power lasers. Its description is theoretically very challenging as it contains correlated quantum electrons at finite temperature—a system that cannot be accurately modeled by standard analytical or ground state approaches. Recently, several breakthroughs have been achieved in the field of fermionic quantum Monte Carlo simulations. First, it was shown that exact simulations of a finite model system ( 30…100 electrons) are possible, which avoid any simplifying approximations such as fixed nodes [Schoof et al., Phys. Rev. Lett. 115, 130402 (2015)]. Second, a novel way to accurately extrapolate these results to the thermodynamic limit was reported by Dornheim et al. [Phys. Rev. Lett. 117, 156403 (2016)]. As a result, now thermodynamic results for the warm dense electron gas are available, w...

Ab initio quantum Monte Carlo simulation of the warm dense electron gas

The uniform electron gas (UEG) at finite temperature is of high current interest due to its key relevance for many applications including dense plasmas and laser excited solids. In particular, density functional theory heavily relies on accurate thermodynamic data for the UEG. Until recently, the only existing first-principle results had been obtained for N = 33 electrons with restricted path integral Monte Carlo (RPIMC), for low to moderate density, rs=r¯/aB≳1. These data have been complemented by configuration path integral Monte Carlo (CPIMC) simulations for rs ≤ 1 that substantially deviate from RPIMC towards smaller rs and low temperature. In this work, we present results from an independent third method—the recently developed permutation blocking path integral Monte Carlo (PB-PIMC) approach [T. Dornheim et al., New J. Phys. 17, 073017 (2015)] which we extend to the UEG. Interestingly, PB-PIMC allows us to perform simulations over the entire density range down to half the Fermi temperature (θ = kBT/EF = 0.5) and, therefore, to compare our results to both aforementioned methods. While we find excellent agreement with CPIMC, where results are available, we observe deviations from RPIMC that are beyond the statistical errors and increase with density.

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Tim Schoof

Papers

Ab Initio Thermodynamic Results for the Degenerate Electron Gas at Finite Temperature.

Configuration Path Integral Monte Carlo

Statically screened ion potential and Bohm potential in a quantum plasma

Ab initio quantum Monte Carlo simulation of the warm dense electron gas

Permutation blocking path integral Monte Carlo approach to the uniform electron gas at finite temperature.