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.
All labels observed (4)
How this entity was disambiguated
This entity first appeared as the object of triple T3576748 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lieb–Liniger model Context triple: [Bethe ansatz, solves, Lieb–Liniger model]
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A.
Gross–Pitaevskii equation
The Gross–Pitaevskii equation is a nonlinear Schrödinger-type equation that describes the macroscopic wavefunction and dynamics of weakly interacting Bose gases at ultra-cold temperatures.
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B.
Luttinger liquid theory
Luttinger liquid theory is a framework describing the collective, non-Fermi-liquid behavior of interacting electrons in one-dimensional conductors, where excitations are best understood as bosonic density waves rather than quasiparticles.
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C.
Bogoliubov theory of weakly interacting Bose gases
Bogoliubov theory of weakly interacting Bose gases is a foundational quantum many-body framework that explains the excitation spectrum and collective behavior of dilute Bose–Einstein condensates by treating interactions as small perturbations around a condensed ground state.
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D.
Fermi gas
A Fermi gas is a quantum many-particle system composed of fermions that obey Fermi–Dirac statistics, often used to model electrons in metals, neutrons in neutron stars, and ultracold atomic gases.
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E.
Bose gas
A Bose gas is a quantum-mechanical system of indistinguishable bosons whose collective behavior is governed by Bose–Einstein statistics, often leading to phenomena like Bose–Einstein condensation at low temperatures.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Lieb–Liniger model Target entity description: 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.
-
A.
Gross–Pitaevskii equation
The Gross–Pitaevskii equation is a nonlinear Schrödinger-type equation that describes the macroscopic wavefunction and dynamics of weakly interacting Bose gases at ultra-cold temperatures.
-
B.
Luttinger liquid theory
Luttinger liquid theory is a framework describing the collective, non-Fermi-liquid behavior of interacting electrons in one-dimensional conductors, where excitations are best understood as bosonic density waves rather than quasiparticles.
-
C.
Bogoliubov theory of weakly interacting Bose gases
Bogoliubov theory of weakly interacting Bose gases is a foundational quantum many-body framework that explains the excitation spectrum and collective behavior of dilute Bose–Einstein condensates by treating interactions as small perturbations around a condensed ground state.
-
D.
Fermi gas
A Fermi gas is a quantum many-particle system composed of fermions that obey Fermi–Dirac statistics, often used to model electrons in metals, neutrons in neutron stars, and ultracold atomic gases.
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E.
Bose gas
A Bose gas is a quantum-mechanical system of indistinguishable bosons whose collective behavior is governed by Bose–Einstein statistics, often leading to phenomena like Bose–Einstein condensation at low temperatures.
- F. None of above. chosen
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 |
continuum Bose gas
ⓘ
linked to:
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 |
Tonks–Girardeau gas
ⓘ
linked to:
Bose 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 equations
ⓘ
linked to:
Yang–Yang equation
|
| introducedIn | 1963 ⓘ |
| isIntegrableIn | one dimension ⓘ |
| namedAfter |
Elliott H. Lieb
ⓘ
Werner Liniger ⓘ |
| publishedIn | Physical Review ⓘ |
| relatedTo |
Bose–Hubbard model in the continuum limit
ⓘ
linked to:
Lieb–Liniger model
Tonks–Girardeau model ⓘ Yang–Yang thermodynamics ⓘ
linked to:
Yang–Yang equation
|
| solvedBy | Bethe ansatz ⓘ |
| usedIn |
cold atom physics
ⓘ
many-body quantum theory ⓘ study of quantum gases ⓘ theory of integrable systems ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Lieb–Liniger model Description of subject: 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.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.
Yang–Yang equation
→
publishedIn
→
Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction
ⓘ
linked to: Lieb–Liniger model
linked to: Lieb–Liniger model
linked to: Lieb–Liniger model