Unity-resolving states and generalised Golden-Thompson bounds on partition functions

Abstract

It is shown that certain sets of normalised unity-resolving (e.g. coherent) states in Hilbert space serve to generate upper bounds on the partition function of a given Hamiltonian in that space. These bounds may be viewed as generalisations of bounds derived previously by Golden, Thompson, Hepp and Lieb (see Phys. Rev. A, vol.8, p.2517, 1973). The new bounds are compared to the original Golden-Thompson bound by proving several theorems and by computing explicit examples.