An Efficient Computational Approach to solve Multi-Orbital Hubbard Model

The study presents a pioneering numerical method for computing Hamiltonian matrix elements of 2D multi-orbital Hubbard clusters. Leveraging Python programming and binary/Boolean logic, this approach offers an innovative solution for tackling the quantum mechanical behavior of interacting electrons in lattice structures. The method's reliability and accuracy are verified by comparing computed energy eigenvalues against exact analytical solutions of single orbital 2-site and 4-site clusters. Notably, this methodology excels in handling larger clusters, overcoming the computational limitations associated with conventional techniques. By utilizing binary integers to represent wavefunctions, the approach enhances computation speed while maintaining low memory usage. This advancement bears significant implications for research in condensed matter physics, quantum computing, and materials science, allowing for efficient exploration of complex 2-dimensional Hubbard clusters. The method's potential extends beyond multi-orbital Hubbard systems, offering a versatile tool for precise and expedient numerical computations across various physics domains.