aiqbench analysis
This research provides a rigorous mathematical classification of minimal three-site spin chains, demonstrating how coupling integrable building blocks can generically destroy integrability in systems beyond nearest-neighbor interactions. By identifying specific models that satisfy or violate criteria like the Reshetikhin condition, the study offers fundamental insights into the mechanisms governing nonintegrability in quantum many-body systems. These findings advance theoretical understanding of exactly solvable and integrable systems, which are foundational for developing advanced quantum simulation algorithms and error-corrected qubit architectures.
Minimal nonintegrable models with three-site interactions
arXiv:2602.07867v2 Announce Type: replace Abstract: We study integrability breaking in translationally invariant spin-$1/2$ chains with genuine three-site interactions. Using a two-qubit composite representation, we prove that the deformed Fredkin spin chain is nonintegrable for any nonzero deformation parameter, although its Hamiltonian decomposes into coupled integrable building blocks. We then extract the minimal injective models, defined as the simplest models needed for a rigorous nonintegrability test, from the Hamiltonian density of the deformed Fredkin spin chain. Among the sixteen such models, six satisfy the Reshetikhin condition and are integrable, while two satisfy Hokkyo's criterion and are nonintegrable away from special coefficient values. Returning to one-site translation-invariant spin-$1/2$ chains leaves four genuine three-site models: two integrable models and two generically nonintegrable models. These results give a compact classification of minimal three-site models obtained from the deformed Fredkin spin chain and identify a local mechanism by which coupling individually integrable structures can destroy integrability beyond nearest-neighbor interactions.
Abstract:We study integrability breaking in translationally invariant spin-$1/2$ chains with genuine three-site interactions. Using a two-qubit composite representation, we prove that the deformed Fredkin spin chain is nonintegrable for any nonzero deformation parameter, although its Hamiltonian decomposes into coupled integrable building blocks. We then extract the minimal injective models, defined as the simplest models needed for a rigorous nonintegrability test, from the Hamiltonian density of the deformed Fredkin spin chain. Among the sixteen such models, six satisfy the Reshetikhin condition and are integrable, while two satisfy Hokkyo's criterion and are nonintegrable away from special coefficient values. Returning to one-site translation-invariant spin-$1/2$ chains leaves four genuine three-site models: two integrable models and two generically nonintegrable models. These results give a compact classification of minimal three-site models obtained from the deformed Fredkin spin chain and identify a local mechanism by which coupling individually integrable structures can destroy integrability beyond nearest-neighbor interactions.
Quantum Physics (quant-ph); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)
arXiv:2602.07867 [quant-ph]
(or arXiv:2602.07867v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2602.07867 Focus to learn more arXiv-issued DOI via DataCite
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