Absence of local conserved quantity in the Heisenberg model with next-nearest-neighbor interaction

Abstract

We rigorously prove that the Heisenberg chain with next-nearest-neighbor interaction, which is anticipated to be non-integrable, is indeed non-integrable in the sense that this system has no nontrivial local conserved quantity. Our result covers two important models, the Majundhar-Ghosh model and the Shastry-Sutherland model, as special cases. These models are shown to be non-integrable while have some solvable energy eigenstates.

27 pages, no figure

References in corpus (9)

• Experimental Observation of a Generalized Gibbs Ensemble
• The Luttinger model following a sudden interaction switch-on
• Proof of absence of local conserved quantities in the mixed-field Ising chain
• Exact matrix product states at the quantum Lifshitz tricritical point in a spin-1/2 zigzag-chain antiferromagnet with anisotropic $\Gamma$-term
• Quantum Violation of Fluctuation-Dissipation Theorem
• Condensation of Anyons in Frustrated Quantum Magnets
• All Local Conserved Quantities of the One-Dimensional Hubbard Model
• Proof of completeness of the local conserved quantities in the one-dimensional Hubbard model
• Matrix product operator representations for the local conserved quantities of the Heisenberg chain

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• Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains
• Absence of nontrivial local conserved quantities in the quantum compass model on the square lattice
• Absence of nontrivial local conserved quantities in the spin-1 bilinear-biquadratic chain and its anisotropic extensions
• Proof of the absence of local conserved quantities in general spin-1/2 chains with symmetric nearest-neighbor interaction
• Complete Classification of Integrability and Non-integrability for Spin-1/2 Chain with Symmetric Nearest-Neighbor Interaction
• Absence of local conserved charges of the Fredkin spin chain and its truncated versions
• Stable infinite-temperature eigenstates in SU(2)-symmetric nonintegrable models
• Temperature and conditions for thermalization after canonical quenches