Nonzero-temperature path-integral method for fermions and bosons: A grand canonical approach

The calculation of the density matrix for fermions and bosons in the grand canonical ensemble allows an efficient way for the inclusion of fermionic and bosonic statistics at all temperatures. It is shown that in a path- integral formulation the one-particle density matrix can be expressed via an integration over a novel representation of the universal temperature-dependent functional. In this paper we discuss a representation for the universal functional in terms of Hankel functions which is convenient for computational applications. Temperature scaling for the universal functional and its derivatives is also introduced thus allowing an efficient rescaling rather then recalculation of the functional at different temperatures. We expect that our method will give rise to a numerically efficient path-integral approach for calculation of a density matrix in the grand canonical ensemble.