Warm dense matter (WDM) is a phase characterized by temperatures of the order of 10,000 K and high nuclei densities. WDM is of high interest in many fields of physics, chemistry, planetary sciences and even industry: from giant gas planets, the earth’s core, laser-heated solids and surfaces, and up to ignition of inertial confinement fusion capsules. Nowadays, using intense lasers, WDM properties can be investigated in the laboratory, thus requiring attention to theoretical research for interpretation and understanding of the results. In terms of tools for theoretical description it is considered a complex regime, being the intermediate between condensed matter physics (i.e, quantum description) and plasma physics (classic thermodynamics). WDM is often described theoretically using finite-temperature Kohn-Sham (KS) density functional theory (DFT) calculations with reasonably good agreement to experiments. DFT calculations in finite (non-zero) temperatures are, however, extremely expensive due to the large number of fractionally occupied KS orbitals involved in them. In fact, the computational cost exhibits exponential scaling with temperature. Orbital-free DFT is often considered a solution to this problem as it uses non-interacting kinetic energy approximations that depends directly on the electronic density, thus avoiding the use of KS orbitals. Stochastic methods, developed recently appear to be a fitting approache to this scaling problem, since it is somewhat of an orbital free KS method. It uses the states occupation operator to calculate the energy, but skips the step of finding the orbitals and finds the electronic density by taking the trace of it using random orbitals. In the poster I will introduce results of the stochastic calculation of the grand canonical free energy with periodic boundary conditions and its first and second derivatives. I will discuss the calculations’ convergence as a function of material density and temperature as well as the computational effort that is required for it.
This is joint work with Daniel Neuhauser (UC Los Angeles), Eran Rabani (UC Berkeley and Lawrence Berkeley National Laboratory), and Roi Baer (The Hebrew University of Jerusalem).
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