Simulations of Dense Hydrogen and Helium Plasmas Without the Fixed-Node Approximation

Quantum Monte Carlo belongs to the most accurate simulation techniques. For Fermi systems, however, its applicability at strong degeneracy is limited by the fermion sign problem. Recently, a significant progress has been achieved for uniform electron gas with configuration path integral Monte Carlo (CPIMC) and permutation blocking (PB-PIMC)~[1]. Both methods are free from uncontrolled errors introduced by the fixed nodes approximations. Here we develop a generalization of the PB-PIMC~[1] suitable for the grandcanonical ensemble and, in combination with the improved Kelbg potential~[2], perform simulations for hydrogen and helium plasmas down to temperatures 3$\cdot 10^{4}$~K. The obtained isotherms of pressure and internal energy are compared with the restricted PIMC~[3] allowing us to conclude on the accuracy of the fixed-node approximation at weak and strong degeneracy, and how the bound state formation affects the results. Some thermodynamic properties are compared with finite temperature DFT simulations~[4]. [1] T.~Dornheim \textit{et al.}, Phys.Rep. {\bf 744}, 1-86(2018); A.~Filinov \textit{et al.}, Phys.Rev.E {\bf 70}, 046411 (2004); [3] B.~Milizer \textit{et al.}, Phys.Rev.B {\bf 84}, 224109 (2011); [4] D.~Knyazev and, P.~Levashov, Phys. Plasmas {\bf 23}, 102708 (2016).