A non-perturbative path-integral based thermal cluster expansion approach for grand partition function of quantum systems

A path-integral based non-perturbative thermal cluster cumulant (PI-TCC) method is presented for thermal averages of quantum many-body hamiltonians. This provides a PI-expression 〈UI〉y of the quantum fluctuation component of the trace of Boltzmann operator with a gaussian measure, involving the fluctuation variable y around each point x0 of the classical centroid path. The T-ordered products of y-variables in UI are evaluated efficiently via a `Wickʹs theoremʹ for the y-variables, which enables us to express 〈UI〉y as the y-average of a y-normal ordered exponential, where only the number component of cumulant survives. The full gpf is obtained as an integral over x0. The gpf of the quartic anharmonic oscillator is computed as an illustration, using an optimal reference frequency Ω(x0) at each x0.