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Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains
exactly-solvable-and-integrable-systemsmathematical-physicsquantum-physicsstatistical-mechanicsstrongly-correlated-electrons
We investigate the integrability and non-integrability of isotropic spin chains with nearest-neighbor interaction with general spin $S$ in terms of the presence or absence of local conserved quantities. We prove a dichotomy theorem that whether a single quantity is zero or not sharply separates two
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