Uncertainty Principle Enhanced Pairing Correlations in Projected Fermi Systems Near Half Filling

TL;DR

This paper reveals that projecting out certain pairs in lattice Fermi systems near half filling enhances pairing correlations, especially in the Hubbard model, without significantly changing the ground state energy, supported by theoretical inequalities and numerical evidence.

Contribution

It introduces the phenomenon of order by projection in lattice Fermi systems and demonstrates enhanced pairing correlations through rigorous inequalities and numerical simulations.

Findings

Enhanced s-wave pairing correlations due to projection

Negligible impact on ground state energy from projection

Numerical evidence of off-diagonal long-range order in a simplified model

Abstract

We point out the curious phenomenon of order by projection in a class of lattice Fermi systems near half filling. Enhanced pairing correlations of extended s-wave Cooper pairs result from the process of projecting out s-wave Cooper pairs, with negligible effect on the ground state energy. The Hubbard model is a particularly nice example of the above phenomenon, which is revealed with the use of rigorous inequalities including the Uncertainty Principle Inequality. In addition, we present numerical evidence that at half filling, a related but simplified model shows ODLRO of extended s-wave Cooper pairs.