arXiv subjects

Travis Sjostrom

Publications and source records attributed to Travis Sjostrom.

14 recordsLinked to original sources

arXiv2019

The Strongly Coupled Electron Liquid: ab initio Path Integral Monte Carlo Simulations and Dielectric Theories

The strongly coupled electron liquid provides a unique opportunity to study the complex interplay of strong coupling with quantum degeneracy effects and thermal excitations. To this end, we carry out extensive \textit{ab initio} path integral Monte Carlo (PIMC) simulations to compute the static structure factor, interaction energy, density response function, and the corresponding static local field correction in the range of $20\leq r_s \leq 100$ and $0.5\leq θ\leq 4$. We subsequently compare these data to several dielectric approximations, and find that different schemes are capable to reproduce different features of the PIMC results at certain parameters. Moreover, we provide a comprehensive data table of interaction energies and compare those to two recent parametrizations of the exchange-correlation free energy, where they are available. Finally, we briefly touch upon the possibility of a charge-density wave. The present study is complementary to previous investigations of the uniform electron gas in the warm dense matter regime and, thus, further completes our current picture of this fundamental model system at finite temperature. All PIMC data are available online.

physics.comp-ph↗

arXiv2017

Sesame-Style Decomposition of KS-DFT Molecular Dynamics for Direct Interrogation of Nuclear Models

A common paradigm used in the construction of equations of state is to decompose the thermodynamics into a superposition of three terms: a static-lattice cold curve, a contribution from the thermal motion of the nuclei, and a contribution from the thermal excitation of the electrons. While statistical mechanical models for crystals provide tractable framework for the nuclear contribution in the solid phase, much less is understood about the nuclear contribution above the melt temperature ($C_v^{(\text{nuc})}\approx 3R$) and how it should transition to the high-temperature limit ($C_v^{(\text{nuc})} \sim \frac{3}{2}R$). In this work, we describe an algorithm for extracting both the thermal nuclear and thermal electronic contributions from quantum molecular dynamics (QMD). We then use the VASP QMD package to probe thermal nuclear behavior of liquid aluminum at normal density to compare the results to semi-empirical models -- the Johnson generic model, the Chisolm high-temperature liquid model, and the CRIS model.

physics.comp-ph↗

arXiv2017

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

In a recent Letter [T.~Dornheim \textit{et al.}, Phys. Rev. Lett. \textbf{117}, 156403 (2016)], we presented the first \textit{ab initio} quantum Monte-Carlo (QMC) results of 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 $θ=k_\text{B}T/E_\text{F}=0.5$ and (ii) of 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 complete \textit{ab initio} exchange-correlation free energy functional; the accuracy achieved is an unprecedented $\sim 0.3\%$. This also allows us to quantify the accuracy and systematic errors of various previous approximate functionals.

physics.plasm-ph↗

arXiv2016

\emph{Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas

Warm dense matter is one of the most active frontiers in plasma physics due to its relevance for dense astrophysical objects as well as 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 ($30 \dots 100$ electrons) is possible that avoid any simplifying approximations such as fixed nodes [Schoof {\em et al.}, Phys. Rev. Lett. {\bf 115}, 130402 (2015)]. Second, a novel way to accurately extrapolate these results to the thermodynamic limit was reported by Dornheim {\em et al.} [Phys. Rev. Lett. {\bf 117}, 156403 (2016)]. As a result, now thermodynamic results for the warm dense electron gas are available that have an unprecedented accuracy on the order of $0.1\%$. Here we present an overview on these results and discuss limitations and future directions.

physics.plasm-ph↗

arXiv2016

{\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit

We perform \emph{ab initio} quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with linear response theory we are able to remove finite-size errors from the potential energy over the entire warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown \emph{et al.}~[PRL \textbf{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 $F_{xc}$ of the macroscopic electron gas with an unprecedented accuracy of $|ΔV|/|V|, |ΔF_{xc}|/|F|_{xc} \sim 10^{-3}$. A comparison of our new data to the recent parametrization of $F_{xc}$ by Karasiev {\em et al.} [PRL {\bf 112}, 076403 (2014)] reveals significant deviations to the latter.

physics.plasm-ph↗

arXiv2015

Ionic and electronic transport properties in dense plasmas by orbital-free density functional theory

We validate the application of our recent orbital-free density functional theory (DFT) approach, [Phys. Rev. Lett. 113, 155006 (2014)], for the calculation of ionic and electronic transport properties of dense plasmas. To this end, we calculate the self-diffusion coefficient, the viscosity coefficient, the electrical and thermal conductivities, and the reflectivity coefficient of hydrogen and aluminum plasmas. Very good agreement is found with orbital-based Kohn-Sham DFT calculations at lower temperatures. Because the method does not scale with temperature, we can produce results at much higher temperatures than is accessible by the Kohn-Sham method. Our results for warm dense aluminum at solid density are inconsistent with the recent experimental results reported by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)].

physics.plasm-ph↗

arXiv2015

Orbital-free extension to Kohn-Sham density functional theory equation of state calculations: application to silicon dioxide

The liquid regime equation of state of silicon dioxide SiO$_2$ is calculated via quantum molecular dynamics in the density range 5 to 15 g/cc and with temperatures from 0.5 to 100 eV, including the $α$-quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data is found to be in very good agreement with the current results. Finally both experimental and simulation data are used in constructing a new liquid regime equation of state table for SiO$_2$.

cond-mat.mtrl-sci↗

arXiv2014

Gradient corrections to the exchange-correlation free energy

We develop the first order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite temperature density functional calculations. Based on this we propose and implement a simple temperature dependent extension for functionals beyond the local density approximation. These finite temperature functionals show improvement over zero temperature functionals as compared to path integral Monte Carlo calculations for deuterium and perform without computational cost increase compared to zero temperature functionals and so should be used for finite temperature calculations.

physics.comp-ph↗

arXiv2014

Fast and accurate quantum molecular dynamics of dense plasmas across temperature regimes

We have developed and implemented a new quantum molecular dynamics approximation that allows fast and accurate simulations of dense plasmas from cold to hot conditions. The method is based on a carefully designed orbital-free implementation of density functional theory (DFT). The results for hydrogen and aluminum are in very good agreement with Kohn-Sham (orbital-based) DFT and path integral Monte Carlo (PIMC) for microscopic features such as the electron density as well as equation of state. The present approach does not scale with temperature and hence extends to higher temperatures than is accessible in Kohn-Sham method and lower temperatures than is accessible by PIMC, while being significantly less computationally expensive than either of those two methods

physics.plasm-ph↗

arXiv2014

Finite-temperature orbital-free DFT molecular dynamics: coupling Profess and Quantum Espresso

Implementation of orbital-free free-energy functionals in the Profess code and the coupling of Profess with the Quantum Espresso code are described. The combination enables orbital-free DFT to drive ab initio molecular dynamics simulations on the same footing (algorithms, thermostats, convergence parameters, etc.) as for Kohn-Sham (KS) DFT. All the non-interacting free-energy functionals implemented are single-point: the local density approximation (LDA; also known as finite-T Thomas-Fermi, ftTF), the second-order gradient approximation (SGA or finite-T gradient-corrected TF), and our recently introduced finite-T generalized gradient approximations (ftGGA). Elimination of the KS orbital bottleneck via orbital-free methodology enables high-T simulations on ordinary computers, whereas those simulations would be costly or even prohibitively time-consuming for KS molecular dynamics (MD) on very high-performance computer systems. Example MD simulations on H over a temperature range 2,000 K <= T <=4,000,000 K are reported, with timings on small clusters (16-128 cores) and even laptops. With respect to KS-driven calculations, the orbital-free calculations are between a few times through a few hundreds of times faster.

cond-mat.mtrl-sci↗

arXiv2014

Local Spin-density Approximation Exchange-correlation Free-energy Functional

An accurate analytical parametrization for the exchange-correlation free energy of the homogeneous electron gas, including interpolation for partial spin-polarization, is derived via thermodynamic analysis of recent restricted path integral Monte-Carlo (RPIMC) data. This parametrization constitutes the local spin density approximation (LSDA) for the exchange-correlation functional in density functional theory. The new finite-temperature LSDA reproduces the RPIMC data well, satisfies the correct high-density and low- and high-$T$ asymptotic limits, and is well-behaved beyond the range of the RPIMC data, suggestive of broad utility.

physics.chem-ph↗

arXiv2013

Uniform electron gas at finite temperatures

We calculate the free energy of the quantum uniform electron gas for temperatures from near zero to 100 times the Fermi energy, approaching the classical limit. An extension of the Vashista-Singwi theory to finite temperatures and self-consistent compressibility sum rule is presented. Comparisons are made to other local field correction methods, as well as recent quantum Monte Carlo simulation and classical map based results. Accurate fits to the exchange-correlation free energy from both theory and simulation are given for future practical applications.

cond-mat.str-el↗

arXiv2012

Comparison of Density Functional Approximations and the Finite-temperature Hartree-Fock Approximation in Warm Dense Lithium

We compare the behavior of the finite-temperature Hartree-Fock model with that of thermal density functional theory using both ground-state and temperature-dependent approximate exchange functionals. The test system is bcc Li in the temperature-density regime of warm dense matter (WDM). In this exchange-only case, there are significant qualitative differences in results from the three approaches. Those differences may be important for Born-Oppenheimer molecular dynamics studies of WDM with ground-state approximate density functionals and thermal occupancies. Such calculations require reliable regularized potentials over a demanding range of temperatures and densities. By comparison of pseudopotential and all-electron results at ${\mathrm T} = 0$K for small Li clusters of local bcc symmetry and bond-lengths equivalent to high density bulk Li, we determine the density ranges for which standard projector augmented wave (PAW) and norm-conserving pseudopotentials are reliable. Then we construct and use all-electron PAW data sets with a small cutoff radius which are valid for lithium densities up to at least 80 g/cm$^3$.

cond-mat.mtrl-sci↗

arXiv2011

Temperature-Dependent Behavior of Confined Many-electron Systems in the Hartree-Fock Approximation

Many-electron systems at substantial finite temperatures and densities present a major challenge to density functional theory. Very little is known about the free-energy behavior over the temperature range of interest, for example, in the study of warm dense matter. As a result, it is difficult to assess the validity of proposed approximate free-energy density functionals. Here we address, at least in part, this need for detailed results on well-characterized systems for purposes of testing and calibration of proposed approximate functionals. We present results on a comparatively simple, well-defined, but computationally feasible model, namely thermally occupied Hartree-Fock states for eight one-electron atoms at arbitrary positions in a hard-walled box. We discuss the main technical tasks (defining a suitable basis and evaluation of the required matrix elements) and discuss the physics which emerges from the calculations.

cond-mat.mtrl-sci↗