Exponential decay of correlation functions in many-electron systems

TL;DR

This paper proves that in certain many-electron models on hyper-cubic lattices, correlation functions decay exponentially with distance at non-zero temperature, under small interaction conditions, using Grassmann integral techniques.

Contribution

It establishes exponential decay bounds for correlation functions in many-electron systems with small interactions, applicable in any dimension and in the thermodynamic limit.

Findings

Correlation functions decay exponentially with distance

Decay bounds hold in all dimensions at non-zero temperature

Results depend on small interaction strength and U(1)-invariance

Abstract

For a class of tight-binding many-electron models on hyper-cubic lattices the equal-time correlation functions at non-zero temperature are proved to decay exponentially in the distance between the center of positions of the electrons and the center of positions of the holes. The decay bounds hold in any space dimension in the thermodynamic limit if the interaction is sufficiently small depending on temperature. The proof is based on the U(1)-invariance property and volume-independent perturbative bounds of the finite dimensional Grassmann integrals formulating the correlation functions.