I have been studying the periodic Anderson model with Holstein phonons to understand the volume collapse mechanisms of the Cerium metal. In order to describe the volume collapse, I need to calculate the pressure versus volume curves for different temperatures. The pressure is obtained from the partial derivative of the free energy with respect to the volume, and thus I need to know the value of free energy as a function of volume for different temperatures.

This program is designed to calculate the energy as a function of temperature and volume from the imaginary frequency Green function. The formula relating the Green function to the total energy can be found in a standard textbook if the phonons are absent. However, our model contains phonons that we have integrated out while doing the Monte Carlo simulation. This integrated out phonons yields a retarded interaction between the electrons. As a result of this, the system cannot be described by a Hamiltonian, but by an effective action obtained from the path integral formalism. I have proved that the total energy formula, the derivation which depends on the existence of a Hamiltonian, can also be used here. This program is a conversion machine that extracts the numerical values of the total energy from abstract mathematical formulae.