Only two models in the class of S=1/2 zigzag spin chains are integrable (one classical, one Bethe-ansatz solvable); all others are non-integrable, with no missing integrable models and no intermediate cases having finitely many local conserved quantities.
How algebraic Bethe ansatz works for integrable model
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
I study the technique of Algebraic Bethe Ansatz for solving integrable models and show how it works in detail on the simplest example of spin 1/2 XXX magnetic chain. Several other models are treated more superficially, only the specific details are given. Several parameters, appearing in these generalizations: spin $s$, anisotropy parameter $\ga$, shift $\om$ in the alternating chain, allow to include in our treatment most known examples of soliton theory, including relativistic model of Quantum Field Theory.
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UNVERDICTED 8representative citing papers
The authors complete the classification of all 4×4 solutions of the quantum Yang-Baxter equation, including non-regular cases, and examine their relation to Lax operators.
Non-Hermitian bosonic chains with symmetric hopping can host k-local charges for selected k only, providing counterexamples to all-or-nothing integrability and showing the Grabowski-Mathieu 3-local test is not universal.
Long-range deformations of arbitrary homogeneous Yang-Baxter integrable spin chains are realized as twists of the quantum group, with the Drinfeld associator encoding the long-range interaction terms up to first order in the deformation parameter.
A Groenewold-Moyal twist deforms an integrable sl(2) spin-chain whose spectrum is computed perturbatively via the Baxter equation and matched at order J^{-3} to a non-local charge of a deformed BMN string in AdS.
Entangling power in Heisenberg spin chains shows a monotonic decrease with growing symmetry in small models, sharp dips at SU(2) and free-fermion points in finite chains, and vanishes at SU(2) points but maximizes at the free-fermion point in the thermodynamic limit for the S-matrix.
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
The quantum compass model on the square lattice possesses no nontrivial local conserved quantities besides the Hamiltonian.
citing papers explorer
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Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
Only two models in the class of S=1/2 zigzag spin chains are integrable (one classical, one Bethe-ansatz solvable); all others are non-integrable, with no missing integrable models and no intermediate cases having finitely many local conserved quantities.
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All 4 x 4 solutions of the quantum Yang-Baxter equation
The authors complete the classification of all 4×4 solutions of the quantum Yang-Baxter equation, including non-regular cases, and examine their relation to Lax operators.
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Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains
Non-Hermitian bosonic chains with symmetric hopping can host k-local charges for selected k only, providing counterexamples to all-or-nothing integrability and showing the Grabowski-Mathieu 3-local test is not universal.
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The quantum group structure of long-range integrable deformations
Long-range deformations of arbitrary homogeneous Yang-Baxter integrable spin chains are realized as twists of the quantum group, with the Drinfeld associator encoding the long-range interaction terms up to first order in the deformation parameter.
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Groenewold-Moyal twists, integrable spin-chains and AdS/CFT
A Groenewold-Moyal twist deforms an integrable sl(2) spin-chain whose spectrum is computed perturbatively via the Baxter equation and matched at order J^{-3} to a non-local charge of a deformed BMN string in AdS.
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Entangling Power: A Probe of Symmetry and Integrability in Quantum Many-Body Systems
Entangling power in Heisenberg spin chains shows a monotonic decrease with growing symmetry in small models, sharp dips at SU(2) and free-fermion points in finite chains, and vanishes at SU(2) points but maximizes at the free-fermion point in the thermodynamic limit for the S-matrix.
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The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
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Absence of nontrivial local conserved quantities in the quantum compass model on the square lattice
The quantum compass model on the square lattice possesses no nontrivial local conserved quantities besides the Hamiltonian.