Bethe ansatz

E75706

exact solution technique method in theoretical physics quantum many-body method

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.

Try in SPARQL Jump to: Surface forms Statements Referenced by

All labels observed (6)

Label	Occurrences
Bethe ansatz canonical	7
algebraic Bethe ansatz	2
coordinate Bethe ansatz	2
Bethe ansatz quantization conditions	1
Bethe equations	1
nested Bethe ansatz	1

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	quantum inverse scattering method ⓘ surface form: algebraic Bethe ansatz Bethe ansatz self-linksurface differs ⓘ surface form: coordinate Bethe ansatz Bethe ansatz self-linksurface differs ⓘ surface form: nested Bethe ansatz off-shell Bethe ansatz ⓘ Yang–Yang equation ⓘ surface form: 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 model ⓘ surface form: 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 (14)

Full triples — surface form annotated when it differs from this entity's canonical label.

Hans Bethe → notableWork → Bethe ansatz ⓘ

Bethe → notableWork → Bethe ansatz ⓘ

subject surface form: Hans Bethe

Bethe ansatz → hasVariant → Bethe ansatz self-linksurface differs ⓘ

this entity surface form: coordinate Bethe ansatz

Bethe ansatz → hasVariant → Bethe ansatz self-linksurface differs ⓘ

this entity surface form: nested Bethe ansatz

Yang–Yang equation → framework → Bethe ansatz ⓘ

Yang–Yang equation → basedOn → Bethe ansatz ⓘ

this entity surface form: Bethe ansatz quantization conditions

Yang–Yang equation → relatedTo → Bethe ansatz ⓘ

this entity surface form: Bethe equations

XXZ spin chain → isExactlySolvableBy → Bethe ansatz ⓘ

Lieb–Liniger model → solvedBy → Bethe ansatz ⓘ

quantum inverse scattering method → relatedTo → Bethe ansatz ⓘ

quantum inverse scattering method → extends → Bethe ansatz ⓘ

quantum inverse scattering method → usesConcept → Bethe ansatz ⓘ

this entity surface form: algebraic Bethe ansatz

quantum inverse scattering method → hasApproach → Bethe ansatz ⓘ

this entity surface form: algebraic Bethe ansatz

quantum inverse scattering method → hasApproach → Bethe ansatz ⓘ

this entity surface form: coordinate Bethe ansatz