Thermal averaging in quantum many-body systems: a non-perturbative thermal cluster cumulant approach

Abstract

We present here a non-perturbative cluster cumulant approach for effecting thermal averaging in quantum-mechanical observables. We introduce a new representation of thermo field dynamics (TFD), with the associated thermal normal order and Wick expansion, and replace the thermal averaging by a quantum mechanical one involving a thermal "base state" |0_β. Unlike the traditional TFD, only the physical variables appear in our formulation. The imaginary time evolution of the statistical operator is treated by our recently developed time-dependent coupled cluster theory. The partition function Z is evaluated as a completely contracted quantity involving |0_β. We have computed Z for an anharmonic oscillator with quartic perturbation as an illustrative application. We also demonstrate numerically the validity of the Kohn-Luttinger theorem.