An analysis of variational wave function for the pairing problem in strongly correlated system

TL;DR

This paper provides a theoretical analysis of variational wave functions for the BCS pairing problem in strongly correlated systems, emphasizing the importance of going beyond traditional approximations to ensure stability.

Contribution

It develops optimized Fermi-Hypernetted Chain equations for variational wave functions, enhancing the understanding of pairing in strongly correlated systems.

Findings

Going beyond Jastrow-Feenberg approximation is essential for stability.

Developed FHNC-EL equations for better variational analysis.

Highlighted the limitations of traditional wave function approximations.

Abstract

We report a theoretical analysis of variational wave functions for the BCS pairing problem. Starting with a Jastrow-Feenberg (or, in a more recent language "fixed-node") wave function for the superfluid state, we develop the full optimized Fermi-Hypernetted Chain (FHNC-EL) equations which sum a local approximation of the parquet-diagrams. Close examination of the procedure reveals that it is essential to go beyond the usual Jastrow-Feenberg approximation to guarantee the correct stability range.