The extended coupled cluster method and the pairing problem

TL;DR

This paper explores various coupled cluster methods for paired fermion systems, focusing on particle number symmetry breaking and restoration, and finds that higher truncation levels improve accuracy with the most straightforward approach being most stable.

Contribution

It introduces and analyzes the application of the extended coupled cluster method to pairing problems, highlighting the effects of particle number symmetry breaking and restoration.

Findings

All methods converge to exact results with higher truncation levels.

Particle number breaking occurs at intermediate truncation levels.

The simplest method is most stable for large systems.

Abstract

We study the application of various forms of the coupled cluster method to systems with paired fermions. The novel element of the analysis is the study of the breaking and eventual restoration of particle number in the CCM variants. We specifically include Arponen's extended coupled cluster method, which describes the normal Hartree-Fock-Bogoliubov mean field at lowest level of truncation. We show that all methods converge to the exact results as we increase the order of truncation, but that the breaking of particle number at an intermediate level means that this convergence occurs in a surprising way. We argue that the most straightforward form of the method seems to be the most stable approach to implement for realistic (large number of particles) pairing problems