Exponential decay of correlation functions in many-electron systems

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.