Date of Original Version
Path-integral Monte Carlo calculations in quantum statistical mechanics have been performed using either discretized methods for Fourier methods. In each of these methods the internal energy has been calculated using either temperature differentiation or direct operation on the density matrix by the Hamiltonian. It is shown that the variance of the internal energy calculated by operation of the Hamiltonian on the density matrix in the Fourier method is independent of the number of Fourier components included in the expansion of the paths for a number of systems. The variance of the internal energy obtained from the other methods is shown to grow with the size of the expansion used for all systems.
J.D. Doll and D.L. Freeman, “A Comparison of Energy Estimators Used in Quantum Monte-Carlo Calculations,” J. Chem. Phys., 83, 768-771 (1985).