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 |
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 |
Drinfeld–Jimbo quantum groups
ⓘ
surface form:
quantum group U_q(sl_2)
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 ⓘ |
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
XXZ Heisenberg model