Jordan–Wigner transformation
E456584
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Jordan–Wigner transformation canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4631892 — 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: Jordan–Wigner transformation Context triple: [Pascual Jordan, notableIdea, Jordan–Wigner transformation]
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A.
Onsager algebra
The Onsager algebra is an infinite-dimensional Lie algebra introduced in the study of exactly solvable models in statistical mechanics, particularly the two-dimensional Ising model.
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B.
Bethe ansatz
The Bethe ansatz is a powerful method in theoretical physics for exactly solving certain one-dimensional quantum many-body systems by reducing them to algebraic equations for particle momenta.
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C.
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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D.
Kramers–Wannier duality in the Ising model
Kramers–Wannier duality in the Ising model is a mathematical transformation that relates the high-temperature and low-temperature phases of the two-dimensional Ising model, revealing the location of its critical point and illustrating a deep symmetry between ordered and disordered states.
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E.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
- 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: Jordan–Wigner transformation Target entity description: 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.
-
A.
Onsager algebra
The Onsager algebra is an infinite-dimensional Lie algebra introduced in the study of exactly solvable models in statistical mechanics, particularly the two-dimensional Ising model.
-
B.
Bethe ansatz
The Bethe ansatz is a powerful method in theoretical physics for exactly solving certain one-dimensional quantum many-body systems by reducing them to algebraic equations for particle momenta.
-
C.
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.
-
D.
Kramers–Wannier duality in the Ising model
Kramers–Wannier duality in the Ising model is a mathematical transformation that relates the high-temperature and low-temperature phases of the two-dimensional Ising model, revealing the location of its critical point and illustrating a deep symmetry between ordered and disordered states.
-
E.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mapping
ⓘ
mathematical transformation ⓘ technique in quantum many-body physics ⓘ |
| appliesTo |
finite one-dimensional lattices
ⓘ
infinite one-dimensional lattices ⓘ |
| assumes | spin-1/2 degrees of freedom on a lattice ⓘ |
| category |
exact transformation
ⓘ
operator mapping ⓘ |
| difficulty | becomes highly nonlocal in higher dimensions ⓘ |
| domain | one-dimensional spin chains ⓘ |
| ensures | correct fermionic sign structure ⓘ |
| field |
condensed matter physics
ⓘ
quantum information theory ⓘ quantum many-body physics ⓘ |
| generalizationOf | spin-fermion correspondence in one dimension ⓘ |
| introduces | nonlocal string operators ⓘ |
| involves |
Pauli matrices σx, σy, σz
ⓘ
linked to:
Pauli matrices
fermionic annihilation operators ⓘ fermionic creation operators ⓘ |
| language | second quantization ⓘ |
| limitation | naturally defined in one spatial dimension ⓘ |
| maps |
spin operators to fermionic operators
ⓘ
spin-1/2 operators to fermionic creation and annihilation operators ⓘ |
| mathematicalForm | string of σz operators multiplying local spin-flip operators ⓘ |
| namedAfter |
Eugene Wigner
ⓘ
Pascual Jordan ⓘ |
| preserves | canonical anticommutation relations of fermions ⓘ |
| property | nonlocal in real space ⓘ |
| relatedTo |
Bogoliubov transformation
ⓘ
Bravyi–Kitaev transformation ⓘ spin–fermion mapping ⓘ |
| relates | Pauli spin matrices to fermionic operators ⓘ |
| requires | an ordering of lattice sites ⓘ |
| usedFor |
diagonalizing quadratic fermionic Hamiltonians
ⓘ
mapping qubit operators to fermionic operators in quantum algorithms ⓘ mapping spin Hamiltonians to quadratic fermionic Hamiltonians ⓘ mapping spin models to fermionic models ⓘ mapping the XY spin chain to fermions ⓘ mapping the transverse-field Ising model to free fermions ⓘ solving one-dimensional quantum spin chains ⓘ studying spin systems with fermionic methods ⓘ |
| usedIn |
exact solution of the one-dimensional XY model
ⓘ
exact solution of the one-dimensional transverse-field Ising model ⓘ mapping spin models to Majorana fermions ⓘ quantum computing encodings of spin systems ⓘ quantum simulation of spin systems with fermionic platforms ⓘ studies of quantum phase transitions in spin chains ⓘ |
| yearProposed | 1928 ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Jordan–Wigner transformation Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.