Hubbard model

Common card · No. 343035

The Hubbard model is a simplified model used to describe the transition between conducting and insulating systems. It is particularly useful in solid-state physics. The model is named after John Hubbard. The Hubbard model states that each electron experiences competing forces: one pushes it to tunnel to neighboring atoms, while the other pushes it away from its neighbors. Its Hamiltonian thus has two terms: a kinetic term allowing for tunneling ("hopping") of particles between lattice sites and a potential term reflecting on-site interaction. The particles can either be fermions, as in Hubbard's original work, or bosons, in which case the model is referred to as the "Bose–Hubbard model". The Hubbard model is a useful approximation for particles in a periodic potential at sufficiently low temperatures, where all the particles may be assumed to be in the lowest Bloch band, and long-range interactions between the particles can be ignored. If interactions between particles at different sites...

Read on Wikipedia · Image Susumu Yamada, Toshiyuki Imamura, Masahiko Machida, CC BY-SA 4.0