Hubbard model

The Hubbard model describes particles hopping between lattice sites while interacting when they occupy the same site. Its competition between kinetic energy and on-site repulsion produces metallic, insulating, and magnetic phases.

Hubbard Hamiltonian: The operator specifying hopping, on-site interactions, and particle energies in the Hubbard model. Its terms make explicit the kinetic-versus-interaction competition at the model’s core.
Fermi–Hubbard model: The Hubbard model for fermions, commonly used to describe electrons in a lattice. Electron applications use fermionic statistics, which restrict occupancy and shape magnetic behavior.
Cuprate superconductors: Copper-oxide materials that superconduct at relatively high temperatures and have strongly correlated electrons. The Hubbard model is a leading framework for studying their insulating parent compounds and doped phases.
John Hubbard: A British theoretical physicist known for work on electron correlations and the model bearing his name. His 1963 papers established the model as a framework for interacting electrons.
Sign problem: A computational obstacle in quantum Monte Carlo caused by cancellations that undermine statistical sampling. It obstructs reliable simulations of the doped two-dimensional Hubbard model at low temperatures.
Tight-binding model: A lattice description in which particles move between sites through specified hopping amplitudes. The Hubbard model adds interactions to this framework for localized particles.
Bose–Hubbard model: The Hubbard model for bosons, describing hopping and repulsion on a lattice. Its bosonic particles provide a distinct realization of the same competing terms.
Ultracold atoms in optical lattices: Laser-generated periodic potentials that trap ultracold atoms in lattice-like arrangements. Experiments can tune hopping and interactions to realize Hubbard-model regimes.
Walter Heitler: A physicist whose quantum theory of chemical bonding helped establish the modern account of exchange interactions. The Hubbard model’s strong-coupling limit connects to exchange physics rooted in this tradition.
d-wave superconductivity: A superconducting state whose order parameter changes sign with direction, commonly associated with cuprates. Whether this pairing emerges from the repulsive Hubbard model remains a central research question.

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