XXZ spin chain
E368993
exactly solvable model
integrable model
lattice model in condensed matter physics
quantum many-body system
quantum spin chain model
The XXZ spin chain is a quantum many-body model of interacting spins on a one-dimensional lattice with anisotropic spin–spin couplings, widely studied in condensed matter physics and exactly solvable by integrable methods.
All labels observed (2)
| Label | Occurrences |
|---|---|
| XXZ spin chain canonical | 3 |
| XXZ Heisenberg model | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3576747 — 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: XXZ spin chain Context triple: [Bethe ansatz, solves, XXZ spin chain]
-
A.
Bethe ansatz
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.
-
B.
Heisenberg model
The Heisenberg model is a fundamental theoretical framework in quantum mechanics and condensed matter physics that describes interacting spins on a lattice and underpins much of our understanding of magnetism in materials.
-
C.
Onsager algebra
The Onsager algebra is an infinite-dimensional Lie algebra introduced in the study of exactly solvable models in statistical mechanics, particularly the two-dimensional Ising model.
-
D.
Kac ring model
The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
-
E.
Yang–Baxter equation
The Yang–Baxter equation is a fundamental consistency condition in mathematical physics and integrable systems that underlies exactly solvable models, quantum groups, and braid group representations.
- 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: XXZ spin chain Target entity description: The XXZ spin chain is a quantum many-body model of interacting spins on a one-dimensional lattice with anisotropic spin–spin couplings, widely studied in condensed matter physics and exactly solvable by integrable methods.
-
A.
Bethe ansatz
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.
-
B.
Heisenberg model
The Heisenberg model is a fundamental theoretical framework in quantum mechanics and condensed matter physics that describes interacting spins on a lattice and underpins much of our understanding of magnetism in materials.
-
C.
Onsager algebra
The Onsager algebra is an infinite-dimensional Lie algebra introduced in the study of exactly solvable models in statistical mechanics, particularly the two-dimensional Ising model.
-
D.
Kac ring model
The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
-
E.
Yang–Baxter equation
The Yang–Baxter equation is a fundamental consistency condition in mathematical physics and integrable systems that underlies exactly solvable models, quantum groups, and braid group representations.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
exactly solvable model
ⓘ
integrable model ⓘ lattice model in condensed matter physics ⓘ quantum many-body system ⓘ quantum spin chain model ⓘ |
| conservesQuantity | total S^z magnetization ⓘ |
| hasAnisotropy | anisotropic spin–spin coupling ⓘ |
| hasAnisotropyParameter | Δ ⓘ |
| hasBoundaryCondition |
open boundary conditions
ⓘ
periodic boundary conditions ⓘ |
| hasConservedQuantities | infinite set of local integrals of motion ⓘ |
| hasCouplingConstant | J ⓘ |
| hasDegreesOfFreedom | spin-1/2 ⓘ |
| hasDimensionality | one-dimensional ⓘ |
| hasExcitations |
magnons
ⓘ
spinons ⓘ |
| hasHamiltonianForm | H = J ∑_i (S_i^x S_{i+1}^x + S_i^y S_{i+1}^y + Δ S_i^z S_{i+1}^z) ⓘ |
| hasHilbertSpace | tensor product of local spin-1/2 spaces ⓘ |
| hasHistoricalOrigin | generalization of the Heisenberg model ⓘ |
| hasInteractionType | nearest-neighbor interaction ⓘ |
| hasLatticeStructure | linear chain ⓘ |
| hasParameterRegime |
easy-axis regime Δ > 1
ⓘ
easy-plane regime |Δ| < 1 ⓘ isotropic point Δ = 1 ⓘ |
| hasPhase |
gapless critical phase for |Δ| ≤ 1
ⓘ
gapped antiferromagnetic phase for Δ > 1 ⓘ gapped ferromagnetic phase for Δ < -1 ⓘ |
| hasRMatrix | trigonometric R-matrix ⓘ |
| hasSymmetry | U(1) symmetry ⓘ |
| hasTransferMatrix | commuting family of transfer matrices ⓘ |
| isDescribedAtLowEnergyBy | Luttinger liquid theory for |Δ| < 1 ⓘ |
| isExactlySolvableBy |
Bethe ansatz
ⓘ
algebraic Bethe ansatz ⓘ coordinate Bethe ansatz ⓘ quantum inverse scattering method ⓘ |
| isIntegrableFor |
certain open boundary conditions
ⓘ
periodic boundary conditions ⓘ |
| isIsingLikeLimit | Ising chain in a transverse field for |Δ| → ∞ (up to scaling) ⓘ |
| isIsotropicLimit | XXX Heisenberg spin chain at Δ = 1 ⓘ |
| isPlanarLimit | XX spin chain at Δ = 0 ⓘ |
| isRelatedTo |
quantum group U_q(sl_2)
ⓘ
linked to:
Drinfeld–Jimbo quantum groups
six-vertex model ⓘ |
| isUsedToStudy |
entanglement in many-body systems
ⓘ
quantum magnetism ⓘ quantum phase transitions ⓘ transport in low-dimensional systems ⓘ |
| isWidelyStudiedIn |
condensed matter physics
ⓘ
mathematical physics ⓘ |
| reducesTo |
XX spin chain
ⓘ
XXX Heisenberg spin chain ⓘ |
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: XXZ spin chain Description of subject: The XXZ spin chain is a quantum many-body model of interacting spins on a one-dimensional lattice with anisotropic spin–spin couplings, widely studied in condensed matter physics and exactly solvable by integrable methods.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: XXZ spin chain