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.

arXiv comment27 pages, no figure

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Cited by in corpus (11)

• Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
• Proof of absence of local conserved quantities in two- and higher-dimensional quantum Ising models
• Macroscopic Irreversibility in Quantum Systems: Free Expansion in a Fermion Chain
• 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