Bethe ansatz
E75706
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.
Aliases (2)
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
exact solution technique
→
method in theoretical physics → quantum many-body method → |
| appliesTo |
exactly solvable models
→
integrable spin chains → one-dimensional quantum many-body systems → quantum lattice models → |
| basedOn |
reduction to algebraic equations for particle momenta
→
|
| characteristicProperty |
absence of particle production in scattering
→
existence of infinitely many conserved quantities in integrable models → factorization of many-body scattering into two-body scattering → |
| computes |
correlation functions in integrable models
→
thermodynamic properties of one-dimensional systems → |
| field |
mathematical physics
→
quantum integrable systems → theoretical physics → |
| hasVariant |
algebraic Bethe ansatz
→
coordinate Bethe ansatz → nested Bethe ansatz → off-shell Bethe ansatz → thermodynamic Bethe ansatz → |
| introducedBy |
Hans Bethe
→
|
| introducedFor |
Heisenberg model
→
|
| introducedIn |
1931
→
|
| relatedTo |
R-matrix formalism
→
Yang–Baxter equation → quantum groups → quantum inverse scattering method → |
| requires |
integrability of the model
→
two-body scattering matrix → |
| solves |
Heisenberg spin chain
→
Hubbard model in one dimension → Lieb–Liniger model → XXX spin chain → XXZ spin chain → one-dimensional Bose gas with delta interaction → |
| usedIn |
AdS/CFT integrability
→
condensed matter physics → quantum field theory → statistical mechanics → string theory → |
| usesConcept |
factorized scattering
→
integrability → periodic boundary conditions → quasi-particles → scattering phases → |
| yields |
Bethe equations
→
eigenstates of the Hamiltonian → exact energy spectra → quantization conditions for momenta → |
Referenced by (4)
| Subject (surface form when different) | Predicate |
|---|---|
|
Bethe ansatz
("coordinate Bethe ansatz")
→
Bethe ansatz ("nested Bethe ansatz") → |
hasVariant |
|
Hans Bethe
→
Hans Bethe → |
notableWork |