quantum inverse scattering method
E368995
algebraic framework
mathematical method
method in quantum integrable systems
technique in mathematical physics
The quantum inverse scattering method is a powerful algebraic framework for solving exactly integrable quantum many-body systems, closely connected to and extending the Bethe ansatz.
All labels observed (2)
| Label | Occurrences |
|---|---|
| algebraic Bethe ansatz | 1 |
| quantum inverse scattering method canonical | 1 |
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic framework
ⓘ
mathematical method ⓘ method in quantum integrable systems ⓘ technique in mathematical physics ⓘ |
| aim | exact solvability of quantum models ⓘ |
| appliesTo |
Heisenberg model
ⓘ
surface form:
Heisenberg spin chain
Lieb–Liniger model ⓘ XXZ spin chain ⓘ XYZ spin chain ⓘ eight-vertex model ⓘ integrable lattice models ⓘ integrable quantum field theories ⓘ six-vertex model ⓘ |
| basedOn | inverse scattering method ⓘ |
| characteristic | reliance on integrability and infinite conserved quantities ⓘ |
| coreIdea |
diagonalization of commuting families of operators
ⓘ
encoding dynamics in monodromy and transfer matrices ⓘ use of R-matrix satisfying Yang–Baxter equation ⓘ |
| developedIn | 1970s ⓘ |
| extends | Bethe ansatz ⓘ |
| field |
integrable systems
ⓘ
mathematical physics ⓘ quantum many-body theory ⓘ theoretical physics ⓘ |
| hasApproach |
Bethe ansatz
ⓘ
surface form:
algebraic Bethe ansatz
analytic Bethe ansatz ⓘ Bethe ansatz ⓘ
surface form:
coordinate Bethe ansatz
|
| notableContributor |
Evgeny Sklyanin
NERFINISHED
ⓘ
Ludwig Faddeev ⓘ
surface form:
L. D. Faddeev
Leon Takhtajan ⓘ Ludwig Faddeev ⓘ |
| relatedTo |
Bethe ansatz
ⓘ
Yangian symmetry ⓘ classical inverse scattering method ⓘ quantum affine algebras ⓘ |
| usedFor |
computing energy spectra of integrable models
ⓘ
constructing exact eigenstates of quantum Hamiltonians ⓘ constructing transfer matrices ⓘ deriving Bethe equations ⓘ solving exactly integrable quantum many-body systems ⓘ studying correlation functions in integrable models ⓘ |
| usesConcept |
Lax operator
ⓘ
R-matrix ⓘ Yang–Baxter equation ⓘ Bethe ansatz ⓘ
surface form:
algebraic Bethe ansatz
monodromy matrix ⓘ quantum groups ⓘ transfer matrix ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
algebraic Bethe ansatz