DERIVATION OF THE SELF-CONSISTENT PHONON THEORY FROM ZUBAREV TYPE GREENS-FUNCTION

We have presented a new method for the derivation of the Helmholtz fre e energy (F) of an anharmonic manic crystal from the Zubarev type Gree n's function. The Hamiltonian (H) employed in the derivation contains the contributions from all the even terms of the Taylor's expansion of the crystal potential energy. In the language of perturbation theory (PT) these are essentially all the first order PT contributions summed to infinity to the free energy, the self-energy of the Green's functi on, and the renormalized phonon frequencies. The self-consistency cond ition arises because in evaluating the correlation functions from the Zubarev type Green's functions the full Hamiltonian is required instea d of the usual harmonic Hamiltonian. The final equations which determi ne F and the self-consistent phonon frequencies are shown to be identi cal to those of the first order self-consistent phonon (SCI) theory.