Finite Temperature Many-Body Theory with the Lipkin Model

We have compared exact numerical results for the Lipkin model at finite temperature with Hartree-Fock theory and with the results of including in addition the ring diagrams. In the simplest version of the Lipkin model the Hartree-Fock approach shows a ``phase transition" which is absent in the exact results. For more realistic cases, Hartree-Fock provides a very good approximation and a modest improvement is obtained by adding the ring diagrams.Comment: 17 pages, NUC-MINN-93/16-T (4 figures obtainable by fax from the authors

Green's function method with energy-independent vertex functions

In conventional Green's function methods the vertex function T is generally energy dependent. However, a model-space Green's function method where the vertex function is manifestly energy independent can be formulated using energy-independent effective interaction theories based on folded diagrams and/or similarity transformations. This is discussed in general and then illustrated for a 1p1h model-space Green's function applied to a solvable Lipkin many-fermion model. The poles of the conventional Green's function are obtained by solving a self-consistent Dyson equation and model space calculations may lead to unphysical poles. For the energy-independent model-space Green's function only the physical poles of the model problem are reproduced and are in satisfactory agreement with the exact excitation energies.Articl