Numerical Investigation of the Cumulant Expansion for Fourier Path Integrals

Abstract

Recent developments associated with the cumulant expansion of the Fourier path integral Monte Carlo method are illustrated numerically using a simple one-dimensional model of a quantum fluid. By calculating the Helmholtz free energy of the model we demonstrate that 1) recently derived approximate asymptotic expressions for the cumulants requiring only one-dimensional quadrature are both accurate and viable, 2) expressions through third-cumulant order are significantly more rapidly convergent than either the primitive Fourier method or the partial average method, and 3) the derived cumulant convergence orders can be verified numerically.