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

Abstract

In this work, a path integral Monte Carlo (PIMC) algorithm for fictitious identical particles (FIP) is proposed by introducing a $ξ$-ensemble and performing PIMC simulations on the resulting $ξ$-ensemble partition function. The PIMC algorithm with the $ξ$-ensemble allows us to obtain the thermodynamic properties of FIP for different $ξ$ 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 $ξ$ value, in the sense that the autocorrelation time of samples belonging to the same $ξ$ 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.