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 these complex systems. Taking advantage of this special mathematical property, we have formulated an equation that the electron Green's function must satisfy. This derivation not only enriches the theoretical foundation of the Hubbard model but also leads to the development of a concise analytical expression for the Mott transition. Our findings pave the way for further exploration and potentially new insights into the dynamics of electron correlations and phase transitions in condensed matter.