A variational approach to the partition function of an interacting many body system

For the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems an improvement with respect to previous formulations is presented. By including anharmonicities and employing a variational approach quantum effects can be treated even at very low temperatures. In order to test its accuracy the novel approach is applied to the exactly solvable Lipkin-Meshkov-Glick model (LMGM). For thermodynamic properties and level densities good agreement with the exact calculations is found.