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

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 work 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 formulated an equation which directly links the electron Green's function to doublon Green's function. Applied to the triangular lattice Hubbard model, our approach yields results consistent with those from state-of-the-art numerical simulations. Our findings open a route to probing electron-correlation dynamics and phase transitions in the Hubbard model, potentially yielding fresh insight into its emergent many-body physics.