Gutzwiller approximation
E484700
The Gutzwiller approximation is a variational method in condensed matter physics used to study strongly correlated electron systems, particularly metal–insulator (Mott) transitions in lattice models like the Hubbard model.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Gutzwiller approximation canonical | 2 |
| Gutzwiller projection | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4975789 — 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: Gutzwiller approximation Context triple: [Mott transition, theoreticalFramework, Gutzwiller approximation]
-
A.
Kirkwood approximation in statistical mechanics
The Kirkwood approximation in statistical mechanics is a method for approximating many-particle correlation functions by expressing higher-order correlations in terms of lower-order ones, simplifying the description of interacting particle systems.
-
B.
Brillouin–Wigner perturbation theory
Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.
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C.
Jordan–Wigner transformation
The Jordan–Wigner transformation is a mathematical mapping in quantum many-body physics that converts spin operators into fermionic creation and annihilation operators, enabling the study of spin systems using fermionic methods.
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D.
Hubbard model
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.
-
E.
Born expansion of Green’s function
The Born expansion of Green’s function is a perturbative series representation used in scattering theory to express the Green’s function as a sum of successive interaction terms.
- 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: Gutzwiller approximation Target entity description: The Gutzwiller approximation is a variational method in condensed matter physics used to study strongly correlated electron systems, particularly metal–insulator (Mott) transitions in lattice models like the Hubbard model.
-
A.
Kirkwood approximation in statistical mechanics
The Kirkwood approximation in statistical mechanics is a method for approximating many-particle correlation functions by expressing higher-order correlations in terms of lower-order ones, simplifying the description of interacting particle systems.
-
B.
Brillouin–Wigner perturbation theory
Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.
-
C.
Jordan–Wigner transformation
The Jordan–Wigner transformation is a mathematical mapping in quantum many-body physics that converts spin operators into fermionic creation and annihilation operators, enabling the study of spin systems using fermionic methods.
-
D.
Hubbard model
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.
-
E.
Born expansion of Green’s function
The Born expansion of Green’s function is a perturbative series representation used in scattering theory to express the Green’s function as a sum of successive interaction terms.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
method in condensed matter physics
ⓘ
theoretical approximation ⓘ variational method ⓘ |
| advantage |
computationally efficient for large systems
ⓘ
provides intuitive picture of correlation effects ⓘ |
| appliedIn |
modeling correlated electrons in narrow bands
ⓘ
theory of heavy-fermion systems ⓘ theory of itinerant ferromagnetism ⓘ theory of transition-metal oxides ⓘ |
| appliedTo |
Hubbard model
NERFINISHED
ⓘ
multi-band Hubbard models ⓘ |
| approximates | expectation values of operators in Gutzwiller wave functions ⓘ |
| assumes |
local interaction terms dominate
ⓘ
variational parameters determined by minimizing ground-state energy ⓘ |
| basedOn | Gutzwiller wave function NERFINISHED ⓘ |
| characteristic |
captures Brinkman–Rice transition in the Hubbard model
ⓘ
captures correlation-induced band narrowing ⓘ introduces renormalization factors for hopping amplitudes ⓘ reduces double occupancy probability ⓘ |
| comparedTo |
exact diagonalization
ⓘ
quantum Monte Carlo methods ⓘ |
| describedIn | Martin C. Gutzwiller’s papers on effect of correlation on ferromagnetism ⓘ |
| developedBy | Martin C. Gutzwiller NERFINISHED ⓘ |
| field | condensed matter physics ⓘ |
| hasVariant |
Gutzwiller approximation for multi-orbital systems
ⓘ
Gutzwiller approximation with spin-rotation invariance ⓘ time-dependent Gutzwiller approximation ⓘ |
| improvesUpon | uncorrelated mean-field descriptions ⓘ |
| influenced | development of modern correlated-electron methods ⓘ |
| limitation |
exact only in infinite spatial dimensions
ⓘ
neglects nonlocal correlations ⓘ static approximation without frequency dependence ⓘ |
| mathematicalForm | renormalization of kinetic and interaction terms by Gutzwiller factors ⓘ |
| publicationYear |
1963
ⓘ
1964 ⓘ |
| relatedTo |
Brinkman–Rice picture of the Mott transition
NERFINISHED
ⓘ
Hartree–Fock approximation NERFINISHED ⓘ dynamical mean-field theory ⓘ slave-boson mean-field theory ⓘ |
| usedFor |
analyzing lattice fermion models
ⓘ
describing metal–insulator transitions ⓘ studying Mott transitions ⓘ studying strongly correlated electron systems ⓘ |
| usesConcept |
local correlation operators
ⓘ
projected wave functions ⓘ variational principle ⓘ |
How these facts were elicited
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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: Gutzwiller approximation Description of subject: The Gutzwiller approximation is a variational method in condensed matter physics used to study strongly correlated electron systems, particularly metal–insulator (Mott) transitions in lattice models like the Hubbard model.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Gutzwiller projection