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 (3)
| Label | Occurrences |
|---|---|
| Gutzwiller approximation canonical | 3 |
| Gutzwiller projection | 2 |
| Gutzwiller wave function | 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.
-
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
- 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
ⓘ
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
ⓘ
linked to:
Gutzwiller approximation
|
| 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
ⓘ
linked to:
Martin Gutzwiller
|
| 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
ⓘ
linked to:
Mott transition
Hartree–Fock approximation ⓘ
linked to:
Hartree–Fock method
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
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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 (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Gutzwiller approximation
linked to: Gutzwiller approximation
linked to: Gutzwiller approximation
subject linked to:
Gutzwiller