Restricted Configuration Path integral Monte Carlo for warm dense matter

Quantum Monte Carlo is the most accurate method for simulating the homogeneous electron gas under warm dense matter conditions [T. Dornheim et al., Phys. Reports 744, 1-86 (2018)] However, due to the notorious fermion sign problem, previous ab initio approaches were restricted to temperatures above half the Fermi temperature, i.e. $\Theta=k_BT/E_F \ge 0.5$. Also, the method of choice for the degenerate Fermi gas -- configuration path integral Monte Carlo (CPIMC) [T. Schoof et al., Contrib. Plasma Phys. 51, 687 (2011)] -- is restricted to high density, i.e. $r_s=\bar r/a_B \le 1$. Here, we construct two new approximations -- RCPIMC and RCPIMC+ -- that neglect some classes of Monte Carlo updates. While RCPIMC+ reduces the sign problem, RPCIMC completely eliminates it, at the price of a systematic error. We investigate the magnitude of the errors by comparing new finite size corrected [T. Dornheim et al., Phys. Rev. Lett. 117, 156403 (2016)] simulations to the parametrization [S. Groth et al., Phys. Rev. Lett. 115, 135001(2017)]. As a result we conclude that RCPIMC+ allows for accurate simulations of thermodynamic properties (deviations of less than $1\%$) at least up to $r_s = 3$ and $0.05 \le \Theta \le 0.3$, significantly extending the range of CPIMC.