Long-Range Correlation of Electron Pairs in the Hubbard Model at Finite Temperatures in Three Dimensions

TL;DR

This study investigates the Hubbard model at finite temperatures in three dimensions, revealing the absence of long-range order in electron pairs, thus challenging its role as a mechanism for superconductivity.

Contribution

It provides a rigorous analysis showing that the Hubbard model does not support long-range electron pair correlations away from half filling at finite temperatures.

Findings

No off-diagonal long-range order of on-site electron pairs

Absence of long-range correlations for nearest-neighbor pairs

Implication against superconductivity mechanisms in the model

Abstract

We show that in the translation invariant case and in the antiferromagnetic phase, the reduced density matrix $\rho _2$ has no off-diagonal long-range order of on-site electron pairs for the single-band Hubbard model on a cubic lattice away from half filling at finite temperatures both for the positive coupling and for the negative coupling. In these cases the model can not give a mechanism for the superconductivity caused by the condensation of on-site electron pairs and the nearest-neighbor electron pairs.