Proof of the Linked-Cluster Expansion in Quantum Statistical Mechanics
Phys. Rev. 116, 21 – Published 1 October, 1959
DOI: https://doi.org/10.1103/PhysRev.116.21
Abstract
In order to go over from a perturbation expansion of the grand partition function (the unlinked-cluster expansion) to an expansion of the thermodynamic potential (the linked-cluster expansion) in powers of the interaction, it is necessary to treat carefully those terms in which creation (or annihilation) operators for the same state occur twice or more. The unlinked- and linked-cluster expansions for a system of fermions are here shown to be equivalent by a direct comparison of the terms which occur in each. The relation between the two expansions is illustrated by the example of a system of fermions interacting only with a single-particle potential.