Particle number renormalization in almost half filled Mott Hubbard superconductors

TL;DR

This paper investigates how Gutzwiller projection affects particle number in BCS wave functions, deriving a fugacity factor and analyzing particle number fluctuations, with implications for variational Monte Carlo methods in strongly correlated superconductors.

Contribution

It introduces a fugacity factor for Gutzwiller projection of BCS states and analyzes particle number effects, enhancing understanding of strongly correlated superconductors.

Findings

Fugacity factor is necessary for Gutzwiller projected BCS wave functions.

Particle number fluctuations are significantly affected by projection.

Differences between canonical and grand canonical projections are highlighted.

Abstract

The effects of the Gutzwiller projection on a BCS wave function with varying particle number are considered. We show that a fugacity factor has to be introduced in these wave functions when they are Gutzwiller projected, and derive an expression for this factor within the Gutzwiller approximation. We examine the effects of the projection operator on BCS wave functions by calculating the average number of particles before and after projection. We also calculate particle number fluctuations in a projected BCS state. Finally, we point out the differences between projecting BCS wave functions in the canonical and grand canonical schemes, and discuss the relevance of our results for variational Monte Carlo studies.