Study of the uniform electron gas through parametrized partition functions

We investigate the energy per particle, static structure factor, and momentum distribution of the uniform electron gas for different conditions defined by the dimensionless temperature $\mathrm{\Theta }=0.25-1.0$ and average interparticle distance $r_s=0.5-80.0$ using path-integral Monte Carlo (PIMC) simulations. For small $r_{\text{s}}$ ($r_{\text{s}}\le 10$) where the sign problem is particularly challenging, we employ a recent approach based on an analytic continuation of the partition function using a real parameter $\xi$, which allows a generalization from bosons ($\xi =1$) to fermions ($\xi =-1$). We show that the results are in good agreement with other state-of-the-art methods while requiring low computational resources. For large $r_{\text{s}}$ ($r_{\text{s}}=80$), we use direct PIMC exploiting the good behaviour of the thermodynamic properties for negative $\xi$. In this framework we demonstrate that, for large $r_s$, the small negative region of $\xi$ can be utilized to extract information about the true fermionic limit, where $\xi =-1$.