Optimal limits on weak integrability breaking and protected thermal memory near qutrit exchange

arXiv:2609.28237v1 Announce Type: cross Abstract: Although integrability does not universally require a continuous one-site symmetry, we rigorously prove that every jointly analytic, regular Yang-Baxter deformation of the qutrit exchange interaction necessarily retains a nontrivial, analytically varying one-site charge. Breaking this local symmetry imposes a fundamental physical constraint on approximate conservation, governed by the optimal uniform bound $\delta^3 \le C\varepsilon$ that explicitly relates the minimal one-site symmetry defect $\delta$ to the local current-conservation residual $\varepsilon$. While breaking all one-site charges strictly forbids an exact integrable completion, an optimally compensated nearest-neighbor interaction saturates this cubic limit and anomalously extends the guaranteed infinite-temperature energy-current correlation window to order $|\lambda|^{-3}$ in the perturbation strength $\lambda$. Furthermore, we reveal a fundamental resonance obstruction for intrinsic conversion perturbations that strictly prevents any exact first-order repair of a broken one-site charge on any finite ring. Nevertheless, we demonstrate that the complete eight-dimensional charge memory matrix remains thermodynamically protected and approaches the identity for timescales $t=o(|\lambda|^{-3/2})$, a robust feature of the full infinite-temperature dynamics when the thermodynamic limit is taken before weak coupling.

Abstract:Although integrability does not universally require a continuous one-site symmetry, we rigorously prove that every jointly analytic, regular Yang-Baxter deformation of the qutrit exchange interaction necessarily retains a nontrivial, analytically varying one-site charge. Breaking this local symmetry imposes a fundamental physical constraint on approximate conservation, governed by the optimal uniform bound $\delta^3 \le C\varepsilon$ that explicitly relates the minimal one-site symmetry defect $\delta$ to the local current-conservation residual $\varepsilon$. While breaking all one-site charges strictly forbids an exact integrable completion, an optimally compensated nearest-neighbor interaction saturates this cubic limit and anomalously extends the guaranteed infinite-temperature energy-current correlation window to order $|\lambda|^{-3}$ in the perturbation strength $\lambda$. Furthermore, we reveal a fundamental resonance obstruction for intrinsic conversion perturbations that strictly prevents any exact first-order repair of a broken one-site charge on any finite ring. Nevertheless, we demonstrate that the complete eight-dimensional charge memory matrix remains thermodynamically protected and approaches the identity for timescales $t=o(|\lambda|^{-3/2})$, a robust feature of the full infinite-temperature dynamics when the thermodynamic limit is taken before weak coupling.

Computational Physics (physics.comp-ph); Statistical Mechanics (cond-mat.stat-mech); Exactly Solvable and Integrable Systems (nlin.SI); Quantum Physics (quant-ph)

arXiv:2609.28237 [physics.comp-ph]

(or arXiv:2609.28237v1 [physics.comp-ph] for this version)

https://doi.org/10.48550/arXiv.2609.28237 arXiv-issued DOI via DataCite (pending registration)

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Optimal limits on weak integrability breaking and protected thermal memory near qutrit exchange

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