三态IRF元胞自动机的局域与准局域守恒律及其量子形变
Local and quasilocal conservation laws of three-state IRF cellular automata and their quantum deformations
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中文总结 AI 辅助
本文研究Klobas等提出的两种三态IRF元胞自动机及其量子形变，明确其守恒律结构，得到欧拉速度下界，支持声活性荷完备性，还发现量子形变的不变态、准模与Mazur界相关性质。
中文摘要 AI 辅助
采用块矩阵乘积方法，我们研究了Klobas和Prosen在[J. Phys. A 55, 094003 (2022)]中提出的两种可逆三态面相互作用（interaction-round-a-face, IRF）元胞自动机——物种守恒规则与物种翻转规则，以及在两者之间插值的相干量子形变。在显式平移不变假设下，两种经典规则共享一个含单参数的准局域守恒律族，其辅助维度为3。每个正则成员也是一个解析辅助维度2族的首个中心对数导数，该族经过恒等可观测量。在该族与三个基本局域荷的闭张空间上，唯一非零欧拉速度为±√(3/23)，因此√(3/23)是任何更大守恒扇区中最大欧拉速度的严格下界。对于物种翻转规则，该值与Klobas和Prosen报告的外推值0.361一致，有力支持了已知声活性荷的完备性。此外，物种守恒规则还允许一个交错生成族，其对数导数形成严格局域荷的无限塔。在量子形变中，相同代数结构产生精确低键维度的不变态（瘢痕候选态）、指数长寿命的准局域准模，以及在从三个基本局域荷投影后产生非零Mazur界的对角准局域荷。
英文摘要
Using patch-matrix-product methods, we study two reversible three-state interaction-round-a-face cellular automata introduced by Klobas and Prosen [J. Phys. A 55, 094003 (2022)] - the species-preserving and species-flipping rules - and a coherent quantum deformation interpolating between them. Within an explicit translationally invariant ansatz, the two classical rules share a one-parameter family of quasi-local conservation laws with an auxiliary-dimension-three realization. Every regular member is also the first centered logarithmic derivative of an analytic auxiliary-dimension-two family passing through the identity observable. On the closed span of this family and the three elementary local charges, the only nonzero Euler velocities are $\pm\sqrt{3/23}$. Consequently, $\sqrt{3/23}$ is a rigorous lower bound on the maximal Euler speed in any larger conserved sector. For the species-flipping rule, this value agrees with the reported extrapolated value $0.361$ of Klobas and Prosen, strongly supporting completeness of the known sound-active charges. The species-preserving rule admits, in addition, a staggered generating family whose logarithmic derivatives form an infinite tower of strictly local charges. In the quantum deformation, the same algebraic structures yield exact low-bond-dimension invariant states (scar candidates), exponentially long-lived quasi-local quasimodes, and diagonal quasi-local charges that produce a nonzero Mazur bound after projection away from the three elementary local charges.
