Exponential decay of equal-time four-point correlation functions in the Hubbard model on the copper-oxide lattice

TL;DR

This paper proves that in the 2D Hubbard model on copper-oxide lattices, equal-time four-point correlation functions decay exponentially with distance under certain temperature and interaction conditions, using multi-scale Matsubara frequency analysis.

Contribution

It provides a rigorous proof of exponential decay of four-point correlations in the Hubbard model under specific regimes, advancing theoretical understanding of high-temperature superconductivity.

Findings

Exponential decay of four-point correlations at positive temperature.

Decay of singlet Cooper pair correlations in high-temperature or weak-coupling regimes.

Use of multi-scale Matsubara frequency integration in the proof.

Abstract

For the Hubbard model on the two-dimensional copper-oxide lattice, equal-time four-point correlation functions at positive temperature are proved to decay exponentially in the thermodynamic limit if the magnitude of the on-site interactions is smaller than some power of temperature. This result especially implies that the equal-time correlation functions for singlet Cooper pairs of various symmetries decay exponentially in the distance between the Cooper pairs in high temperatures or in low-temperature weak-coupling regimes. The proof is based on a multi-scale integration over the Matsubara frequency.