On new efficient algorithms for PIMC and PIMD The properties of various algorithms, estimators, and high-temperature density matrix (HTDM) decompositions relevant for path integral simulations are discussed. It is shown that Fourier accelerated path integral molecular dynamics (PIMD) completely eliminates slowing down with increasing Trotter number $P$. A new primitive estimator of the kinetic energy for use in PIMD simulations is found to behave less pathologically than the original virial estimator. In particular, its variance does not increase significantly with $P$. Two non-primitive HTDM decompositions are compared as well: one decomposition used in the Takahashi Imada algorithm and another one based on an effective propagator. In the latter case, effective potentials are constructed between two particles such that two-particle propagators are reflected exactly -- even at finite $P$.
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