Lieb–Liniger model

E368994

exactly solvable model integrable model model of interacting bosons one-dimensional quantum system quantum many-body model

The Lieb–Liniger model is an exactly solvable quantum many-body system describing one-dimensional bosons with delta-function interactions, fundamental in the study of integrable systems and quantum gases.

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All labels observed (4)

Label	Occurrences
Lieb–Liniger model canonical	3
Bose–Hubbard model in the continuum limit	1
Lieb–Liniger equations	1
Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction	1

Statements (52)

Predicate	Object
instanceOf	exactly solvable model ⓘ integrable model ⓘ model of interacting bosons ⓘ one-dimensional quantum system ⓘ quantum many-body model ⓘ
applicableTo	quasi-one-dimensional Bose gases ⓘ ultracold atoms in tight waveguides ⓘ
describes	one-dimensional bosons with delta-function interactions ⓘ
fieldOfStudy	condensed matter physics ⓘ mathematical physics ⓘ theoretical physics ⓘ
governs	quantum gases in one dimension ⓘ
hasBetheEquations	logarithmic Bethe equations for rapidities ⓘ
hasBoundaryConditions	typically periodic boundary conditions ⓘ
hasConservedQuantities	infinite set of local integrals of motion ⓘ
hasContinuityEquation	for particle density ⓘ
hasContinuumLimit	Bose gas ⓘ surface form: continuum Bose gas
hasCorrelationFunctions	exactly computable in principle ⓘ
hasCouplingConstant	contact interaction strength c ⓘ
hasEnergySpectrum	determined by Bethe equations ⓘ
hasExcitations	hole-like excitations ⓘ particle-like excitations ⓘ
hasGroundState	Bethe-ansatz ground state ⓘ
hasHamiltonianForm	kinetic energy plus delta-function interaction ⓘ
hasInteractionPotential	delta-function potential ⓘ
hasInteractionType	contact interaction ⓘ
hasLimit	Bose gas ⓘ surface form: Tonks–Girardeau gas weakly interacting Bose gas ⓘ
hasParameter	dimensionless interaction parameter γ ⓘ
hasParticleStatistics	bosonic ⓘ
hasPhenomenon	super-Tonks–Girardeau regime in strongly attractive case ⓘ
hasRegime	attractive interaction regime ⓘ repulsive interaction regime ⓘ
hasSolutionType	Bethe-ansatz eigenstates ⓘ
hasSpatialDimension	one-dimensional ⓘ
hasStatistics	Bethe-ansatz rapidity distribution ⓘ
hasSymmetry	Galilean invariance in one dimension ⓘ U(1) particle-number conservation ⓘ
hasThermodynamicDescription	Yang–Yang equation ⓘ surface form: Yang–Yang equations
introducedIn	1963 ⓘ
isIntegrableIn	one dimension ⓘ
namedAfter	Elliott H. Lieb ⓘ Werner Liniger NERFINISHED ⓘ
publishedIn	Physical Review ⓘ
relatedTo	Lieb–Liniger model self-linksurface differs ⓘ surface form: Bose–Hubbard model in the continuum limit Tonks–Girardeau model ⓘ Yang–Yang equation ⓘ surface form: Yang–Yang thermodynamics
solvedBy	Bethe ansatz ⓘ
usedIn	cold atom physics ⓘ many-body quantum theory ⓘ study of quantum gases ⓘ theory of integrable systems ⓘ

Referenced by (6)

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

Bethe ansatz → solves → Lieb–Liniger model ⓘ

Yang–Yang equation → appliesTo → Lieb–Liniger model ⓘ

Yang–Yang equation → publishedIn → Lieb–Liniger model ⓘ

this entity surface form: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction

Yang–Yang equation → relatedTo → Lieb–Liniger model ⓘ

this entity surface form: Lieb–Liniger equations

Lieb–Liniger model → relatedTo → Lieb–Liniger model self-linksurface differs ⓘ

this entity surface form: Bose–Hubbard model in the continuum limit

quantum inverse scattering method → appliesTo → Lieb–Liniger model ⓘ