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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Hubbard model canonical | 4 |
How this entity was disambiguated
This entity first appeared as the object of triple T4537416 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hubbard model Context triple: [Heisenberg model, relatedTo, Hubbard model]
-
A.
Mott insulator
A Mott insulator is a material that, despite having partially filled electronic bands that should allow conduction, behaves as an electrical insulator due to strong electron–electron interactions.
-
B.
Mott transition
The Mott transition is a metal–insulator transition in strongly correlated electron systems, where electron–electron interactions drive a material from conducting to insulating behavior without a change in its crystal structure.
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C.
Heisenberg model
The Heisenberg model is a fundamental theoretical framework in quantum mechanics and condensed matter physics that describes interacting spins on a lattice and underpins much of our understanding of magnetism in materials.
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D.
Luttinger liquid theory
Luttinger liquid theory is a framework describing the collective, non-Fermi-liquid behavior of interacting electrons in one-dimensional conductors, where excitations are best understood as bosonic density waves rather than quasiparticles.
-
E.
Peierls transition
The Peierls transition is a phase transition in one-dimensional metals where a periodic lattice distortion opens an energy gap at the Fermi surface, turning the system from a metal into an insulator or semiconductor.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hubbard model Target entity description: 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.
-
A.
Mott insulator
A Mott insulator is a material that, despite having partially filled electronic bands that should allow conduction, behaves as an electrical insulator due to strong electron–electron interactions.
-
B.
Mott transition
The Mott transition is a metal–insulator transition in strongly correlated electron systems, where electron–electron interactions drive a material from conducting to insulating behavior without a change in its crystal structure.
-
C.
Heisenberg model
The Heisenberg model is a fundamental theoretical framework in quantum mechanics and condensed matter physics that describes interacting spins on a lattice and underpins much of our understanding of magnetism in materials.
-
D.
Luttinger liquid theory
Luttinger liquid theory is a framework describing the collective, non-Fermi-liquid behavior of interacting electrons in one-dimensional conductors, where excitations are best understood as bosonic density waves rather than quasiparticles.
-
E.
Peierls transition
The Peierls transition is a phase transition in one-dimensional metals where a periodic lattice distortion opens an energy gap at the Fermi surface, turning the system from a metal into an insulator or semiconductor.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Hubbard model Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.