The Hubbard Model

The Hubbard Model is a mathematical framework used in condensed matter physics to study the behavior of electrons in materials, especially in solids. It captures how electrons interact with each other and how they move through a lattice or grid of atoms. Specifically, it balances two key aspects: the tendency of electrons to spread out to minimize energy (hopping) and their tendency to avoid each other due to repulsion (on-site interaction). This model helps researchers understand phenomena like magnetism, superconductivity, and metal-insulator transitions in various materials.