Decay of Superconducting and Magnetic Correlations in One- and Two-Dimensional Hubbard Models

TL;DR

This paper establishes upper bounds on correlation functions in 1D and 2D Hubbard models, showing exponential decay in 1D and power-law decay in 2D, thus ruling out certain types of long-range order at finite temperatures.

Contribution

It provides a rigorous mathematical proof of decay bounds for correlations in Hubbard models, applicable to related models like the t-J model.

Findings

Exponential decay of correlations in 1D Hubbard models.

Power-law decay of correlations in 2D Hubbard models.

Ruling out superconducting and magnetic long-range order at finite temperatures.

Abstract

In a general class of one and two dimensional Hubbard models, we prove upper bounds for the two-point correlation functions at finite temperatures for electrons, for electron pairs, and for spins. The upper bounds decay exponentially in one dimension, and with power laws in two dimensions. The bounds rule out the possibility of the corresponding condensation of superconducting electron pairs, and of the corresponding magnetic ordering. Our method is general enough to cover other models such as the t-J model.