Rayleigh-Schroedinger-Goldstone variational perturbation theory for many fermion systems

Details Rayleigh-Schroedinger-Goldstone variational perturbation theory for many fermion systems Rayleigh-Schroedinger-Goldstone variational perturbation theory for many fermion systems

2004-03-30

arxiv.org/abs/cond-mat/0403728v1

Physics

Condensed Matter

Superconductivity

11pages, 1figure

Scientific paper

10.1140/epjb/e2005-00069-7

We present a Rayleigh-Schroedinger-Goldstone perturbation formalism for many fermion systems. Based on this formalism, variational perturbation scheme which goes beyond the Gaussian approximation is developed. In order to go beyond the Gaussian approximation, we identify a parent Hamiltonian which has an effective Gaussian vacuum as a variational solution and carry out further perturbation with respect to the renormalized interaction using Goldstone's expansion. Perturbation rules for the ground state wavefunctional and energy are found. Useful commuting relations between operators and the Gaussian wavefunctional are also found, which could reduce the calculational efforts substantially. As examples, we calculate the first order correction to the Gaussian wavefunctional and the second order correction to the ground state of an electron gas system with the Yukawa-type interaction.

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