Inverted duality of Hubbard model and an equation for the Green's function

The Hubbard model, a cornerstone in the field of condensed matter physics, serves as a fundamental framework for investigating the behavior of strongly correlated electron systems. This paper presents a novel perspective on the model, uncovering its inherent inverted duality which has profound implications for our comprehension of this complex system. Taking advantage of this special mathematical property, we have formulated an equation that the electron Green's function must satisfy. Our findings pave the way for further exploration and potentially new insights into the dynamics of electron correlations and phase transitions in the Hubbard model.