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

TL;DR

This paper develops a novel variational perturbation theory for many fermion systems, extending beyond Gaussian approximations by identifying a suitable parent Hamiltonian and applying Goldstone's expansion.

Contribution

It introduces a new perturbation formalism for fermion systems that surpasses Gaussian approximation, including explicit rules and corrections for ground state calculations.

Findings

First order correction to Gaussian wavefunctional calculated

Second order correction to ground state obtained for electron gas

Perturbation rules simplify calculations significantly

Abstract

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.