Extension of the New Tamm-Dancoff method to phase transitions in many-body systems

H. Mitter, K. Yamazaki

Behram N. Kurșunoǧlu

A. Friederich, W. Gerling, K. Bleuler

Abstract We extend the New Tamm-Dancoff method by introducing intermediate states. In this way we are able to treat with the Green's function method the effect of nearby levels in many-body systems. We formulate the η-and the ζ-function method with intermediate states. Aldready in first order, the ζ-function method yields a whole series of new approximations in addition to known theories such as the Hartree-Fock theory and the Hartree-Bogoliubov theory. As an example we study intensively "the Hartree-Fock theory with intermediate states". The ζ-function method which is based on the η-function method yields in first order in addition to RPA, quasi-particle RPA and other approximations "RPA with intermediate states". We apply the Hartree-Fock theory with intermediate states and RPA with intermediate states to the exactly solvable Lipkin model.

武 辰巳

A. Friederich, W. Gerling

Abstract Instead of emphasizing the ground state as is done in Green's function method, we take a finite-dimensional subspace of the Hilbert space: the space of the "intermediate states". A systematic introduction of intermediate states is effected by an extension of the method of generating functionals: we combine the generating functionals of the n-point Green's functions to a "matrix functional" T, and form new matrix functionals, which are matrix functions of T. The aim of this paper is to develop the functional calculus in such a way that the transition from scalar functionals to matrix functionals is straightforward, and the method of obtaining further results becomes clear. Following the lines of Dürr and Wagner we get u η-and ζ-rules with intermediate states". Using them we define a truncation procedure for the equations of motion of the n-point Green's functions, the "New Tamm-Dancoff method with intermediate states". This extension makes it possible to treat the effect of nearby levels in many body systems with Green's functions. In ad-dition to well-known approximations, such as the Hartree-Fock and the Hartree-Bogoliubov theory, the RPA and the quasiparticle RPA, we obtain a series of new approximations. Among these are the "Hartree-Fock theory with intermediate states" and the "random-phase approximation with intermediate states", which we already applied with great success to some exactly soluble models.

R.K. Pathria, Paul D. Beale