Exact Solution of the 2D/3D Hubbard Model and Bottom-up Design of Room-Temperature Superconductors via Seonggil Theoretical Frameworks

Abstract

The exponential explosion of the Hilbert space and the Fermion Sign Problem have long prevented exact solutions to the 2D and 3D Hubbard models in strongly correlated electron systems. By elevating classical creation/annihilation operators to Rough Fermionic Operators within the Rough Operator Algebra (ROA) framework, and utilizing the Seonggil Matrix Theory for dimensionality reduction, we present an exact closed-form solution. This approach successfully collapses the exponential computational complexity into a polynomial time O(N^k) solvable domain. Furthermore, we derive a generalized macroscopic coherence gap equation, providing a mathematical foundation for the bottom-up design of Room Temperature and Ambient-Pressure Superconductors (RTSC).