Optimal limits on weak integrability breaking and protected thermal memory near qutrit exchange
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 δ3 ≤ Cε that explicitly relates the minimal one-site symmetry defect δ to the local current-conservation residual ε. 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 |λ|−3 in the perturbation strength λ. 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(|λ|−3/2), a robust feature of the full infinite-temperature dynamics when the thermodynamic limit is taken before weak coupling.
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BibTeX
@misc{liang2026optimal,
title = {{Optimal limits on weak integrability breaking and protected thermal memory near qutrit exchange}},
author = {Hanbing Liang and Fujun Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28237},
eprint = {2609.28237},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28237},
}
RIS
TY - UNPB
TI - Optimal limits on weak integrability breaking and protected thermal memory near qutrit exchange
AU - Hanbing Liang
AU - Fujun Liu
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28237
UR - https://arxiv.org/abs/2609.28237
AB - 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 δ^3 ≤ Cε that explicitly relates the minimal one-site symmetry defect δ to the local current-conservation residual ε. 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 |λ|^−3 in the perturbation strength λ. 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(|λ|^−3/2), a robust feature of the full infinite-temperature dynamics when the thermodynamic limit is taken before weak coupling.
ER -