Hubbard model
E450154
The Hubbard model is a fundamental theoretical model in condensed matter physics that describes interacting electrons on a lattice and is widely used to study phenomena such as magnetism, metal–insulator transitions, and high-temperature superconductivity.
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
lattice model
ⓘ
model in condensed matter physics ⓘ theoretical model ⓘ |
| assumes |
electrons move on discrete lattice sites
ⓘ
short-range (on-site) electron–electron interaction ⓘ |
| describes | interacting electrons on a lattice ⓘ |
| exactlySolvableIn | one dimension by Bethe ansatz ⓘ |
| exhibits |
Mott metal–insulator transition
ⓘ
antiferromagnetic order at half filling (for repulsive U) ⓘ spin-charge separation in one dimension ⓘ superconducting correlations (for attractive or effective attraction) ⓘ |
| field | condensed matter physics ⓘ |
| generalizationOf | tight-binding model ⓘ |
| governingHamiltonian | tight-binding term plus on-site interaction term ⓘ |
| hasParameter |
chemical potential μ
ⓘ
electron filling ⓘ hopping amplitude t ⓘ lattice geometry ⓘ on-site interaction U ⓘ |
| hasVariant |
Hubbard model with next-nearest-neighbor hopping
ⓘ
attractive Hubbard model ⓘ disordered Hubbard model ⓘ multi-orbital Hubbard model NERFINISHED ⓘ one-dimensional Hubbard model NERFINISHED ⓘ repulsive Hubbard model ⓘ two-dimensional Hubbard model NERFINISHED ⓘ |
| includesTerm |
nearest-neighbor hopping term
ⓘ
on-site Coulomb repulsion term ⓘ |
| introducedIn | 1960s ⓘ |
| namedAfter | John Hubbard NERFINISHED ⓘ |
| relatedTo |
Anderson impurity model
NERFINISHED
ⓘ
Heisenberg model in large-U limit at half filling ⓘ t-J model NERFINISHED ⓘ |
| relevantFor |
cuprate superconductors
ⓘ
organic conductors ⓘ transition metal oxides ⓘ ultracold atoms in optical lattices ⓘ |
| simplifies | full Coulomb interaction to on-site term U ⓘ |
| studiedUsing |
density matrix renormalization group
ⓘ
dynamical mean-field theory ⓘ exact diagonalization ⓘ quantum Monte Carlo methods ⓘ variational methods ⓘ |
| usedFor |
studying Mott insulators
ⓘ
studying electronic correlations ⓘ studying high-temperature superconductivity ⓘ studying magnetism ⓘ studying metal–insulator transitions ⓘ studying quantum phase transitions ⓘ studying strongly correlated electron systems ⓘ |
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.