标题： 相互作用可积模型中局部算符纠缠的长时间极限 显示英文标题

标题： Long-Time Limits of Local Operator Entanglement in Interacting Integrable Models

摘要： 我们研究有限尺寸相互作用可积系统中局部算子纠缠熵（LOE）的长期行为。 对于规则54自动机中的某些算子，我们证明LOE会趋于一个最多与系统尺寸对数相关的值。 这个对数界限依赖于规则54的一个特性，该特性无法推广到其他相互作用可积系统：即只有两种准粒子，因此准粒子之间的相移只有两种可能的值。 我们提出一个启发式论证，并通过数值证据支持，对于一般的相互作用可积系统（如海森堡自旋链），LOE的饱和值与系统尺寸呈体积定律。 显示英文摘要

摘要： We explore the long-time behavior of Local Operator Entanglement entropy (LOE) in finite-size interacting integrable systems. For certain operators in the Rule 54 automaton, we prove that the LOE saturates to a value that is at most logarithmic in system size. The logarithmic bound relies on a feature of Rule 54 that does not generalize to other interacting integrable systems: namely, that there are only two types of quasiparticles, and therefore only two possible values of the phase shift between quasiparticles. We present a heuristic argument, supported by numerical evidence, that for generic interacting integrable systems (such as the Heisenberg spin chain) the saturated value of the LOE is volume-law in system size.