Integrability Test for Spin Chains

Abstract

We examine a simple heuristic test of integrability for quantum chains. This test is applied to a variety of systems, including a generic isotropic spin-1 model with nearest-neighbor interactions and a multiparameter family of spin-1/2 models generalizing the XYZ chain, with next-to-nearest neighbor interactions and bond alternation. Within the latter family we determine all the integrable models with an o(2) symmetry.

29 pages in plain TeX plus 1 uuencoded figure, uses macros harvmac.tex and epsf.tex

References in corpus (2)

• Quantum Integrals of Motion for the Heisenberg Spin Chain
• Singular Vectors and Conservation Laws of Quantum KdV type equations

Cited by in corpus (46)

• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Remarks on the notion of quantum integrability
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
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• Integrability and Transcendentality
• Spin conductivity in almost integrable spin chains
• Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory
• Yang-Baxter and the Boost: splitting the difference
• The su(N) XX model
• Classifying nearest-neighbour interactions and deformations of AdS
• Classifying integrable spin-1/2 chains with nearest neighbour interactions
• Proof of the absence of local conserved quantities in the XYZ chain with a magnetic field
• Higher-Loop Integrability in N=4 Gauge Theory
• Weak integrability breaking perturbations of integrable models
• Spin chains with dynamical lattice supersymmetry
• Integrable hard rod deformation of the Heisenberg spin chains
• The su(N) Hubbard model
• Factorized world-sheet scattering in near-flat AdS_5 x S^5
• Yangian Symmetry of Long-Range gl(N) Integrable Spin Chains
• Introduction to classical and quantum integrability
• Proof of absence of local conserved quantities in the mixed-field Ising chain
• Quantum many-body scars in spin models with multibody interactions
• The Structure of Conserved Charges in Open Spin Chains
• On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group
• Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains
• Absence of local conserved quantity in the Heisenberg model with next-nearest-neighbor interaction
• Emergent strong zero mode through local Floquet engineering
• Integrable spin chains and the Clifford group
• Free fermions beyond Jordan and Wigner
• Integrable spin chains and cellular automata with medium range interaction
• On the breakdown of perturbative integrability in large N matrix models
• Exactly soluble isotropic spin-1/2 ladder models
• Integrability and the AdS/CFT correspondence
• Higher Charges in Dynamical Spin Chains for SYM Theory
• Exactly solvable subspaces of non-integrable spin chains with boundaries and quasiparticle interactions
• Proof of completeness of the local conserved quantities in the one-dimensional Hubbard model
• Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
• Integrable models on Rydberg atom chains
• New symmetries of the chiral Potts model
• Integrability from a single conservation law in quantum spin chains
• Absence of nontrivial local conserved quantities in the quantum compass model on the square lattice
• Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains
• $G_2$ Integrable Point Characterization via Isotropic Spin-3 Chains
• Complete Classification of Integrability and Non-integrability for Spin-1/2 Chain with Symmetric Nearest-Neighbor Interaction
• Stable infinite-temperature eigenstates in SU(2)-symmetric nonintegrable models
• Absence of local conserved charges of the Fredkin spin chain and its truncated versions