Path Integral Monte Carlo for Fictitious Identical Particles with ξ-Ensemble

In this work, a path integral Monte Carlo (PIMC) algorithm for fictitious identical particles (FIP) is proposed by introducing a $\xi$-ensemble and performing PIMC simulations on the resulting $\xi$-ensemble partition function. The PIMC algorithm with the $\xi$-ensemble allows us to obtain the thermodynamic properties of FIP for different $\xi$ values in a single simulation. Moreover, it also accelerates the simulation by improving the sampling efficiency, compared to the usual case where independent simulations are performed for each $\xi$ value, in the sense that the autocorrelation time of samples belonging to the same $\xi$ sector is decreased. Simulations of the uniform electron gas and uniform warm dense beryllium are performed to validate the improved algorithm and study the improvement in its sampling efficiency.