An extension of the coupled-cluster method: A variational formalism

TL;DR

This paper extends the coupled-cluster method to a variational formalism, introducing new distribution functions and equations, and demonstrates its application to a quantum antiferromagnetic spin model.

Contribution

It develops a variational extension of the coupled-cluster method with a novel algebraic approach and compares it to existing approximations.

Findings

Equivalent to a linear approximation of traditional CCM

Corresponds to a random-phase approximation in the extended formalism

Successfully applied to a quantum antiferromagnetic spin model

Abstract

A general quantum many-body theory in configuration space is developed by extending the traditional coupled cluter method (CCM) to a variational formalism. Two independent sets of distribution functions are introduced to evaluate the Hamiltonian expectation. An algebraic technique for calculating these distribution functions via two self-consistent sets of equations is given. By comparing with the traditional CCM and with Arponen's extension, it is shown that the former is equivalent to a linear approximation to one set of distribution functions and the later is equivalent to a random-phase approximation to it. In additional to these two approximations, other higher-order approximation schemes within the new formalism are also discussed. As a demonstration, we apply this technique to a quantum antiferromagnetic spin model.