Quantum Monte Carlo techniques and applications for warm dense matter

The Quantum Monte Carlo (QMC) method is used to study physical problems which are analytically intractable due to many-body interactions and strong coupling strengths. This makes QMC a natural choice in the warm dense matter (WDM) regime where both the Coulomb coupling parameter Γ ≡ e/(rskBT ) and the electron degeneracy parameter Θ ≡ T/TF are close to unity. As a truly firstprinciples simulation method, it affords superior accuracy while still maintaining reasonable scaling, emphasizing its role as a benchmark tool. Here we give an overview of QMC methods including diffusion MC, path integral MC, and coupled electron-ion MC. We then provide several examples of their use in the WDM regime, reviewing applications to the electron gas, hydrogen plasma, and first row elements. We conclude with a comparison of QMC to other existing methods, touching specifically on QMC’s range of applicability. Ethan Brown Lawrence Livermore National Laboratory, 7000 East Ave., Livermore CA, 94550 and Department of Physics, University of Illinois Urbana-Champaign, 1110 W. Green St. , Urbana, IL 61801-3080, USA e-mail: [email protected] Miguel A. Morales Lawrence Livermore National Laboratory, 7000 East Ave., Livermore CA, 94550 e-mail: [email protected] Carlo Pierleoni Dipartimento di Scienze Fisiche e Chimiche, Universita dell’Aquila and CNISM, UdR dell’Aquila, a V. Vetoio 10, Loc. Coppito, I-67100 L’Aquila, Italy e-mail: [email protected] David Ceperley Department of Physics, University of Illinois Urbana-Champaign, 1110 W. Green St. , Urbana, IL 61801-3080, USA e-mail: [email protected]