A Stochastic approach to thermal DFT

Despite progress in observational astronomy, some elements such as the internal composition of planets are still not well-understood. A root cause is our limited understanding of matter under extreme conditions (MEC) - pressures in the GPa-TPa range and temperatures (T) up to 10⁵ K. Due to the difficulty in preparing MECs, the experimental input is limited, and ab initio calculations are sometimes the only source of information. The Kohn-Sham density functional theory (KS-DFT) seems as a reliable and useful tool for obtaining information on MEC. Calculations in finite temperatures, however, are expensive due to the large number of fractionally occupied KS orbitals involved. A stochastic method developed recently^[1],[2], appears to be a fitting approach to this problem. By performing a stochastic trace, the KS Hamiltonian is directly obtained from the density, resulting in a scaling of T^-1.
I will introduce the convergence and errors involved in calculations of the canonical free energy. In addition, a stochastic approach to calculate the Kubo-Greenwood conductivity will be presented.


[1] R. Baer, D. Neuhauser, E. Rabani, Phys. Rev. Lett. 111, 106402 (2013)

[2]Yael Cytter, Eran Rabani, Daniel Neuhauser, and Roi Baer Phys. Rev. B 97, 115207 (2018)