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.
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
NERFINISHED
ⓘ
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
NERFINISHED
ⓘ
Pascual Jordan NERFINISHED ⓘ |
| preserves | canonical anticommutation relations of fermions ⓘ |
| property | nonlocal in real space ⓘ |
| relatedTo |
Bogoliubov transformation
NERFINISHED
ⓘ
Bravyi–Kitaev transformation NERFINISHED ⓘ 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 ⓘ |
Referenced by (1)
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