论文标题
扩散和操作员纠缠蔓延
Diffusion and operator entanglement spreading
论文作者
论文摘要
了解操作员空间纠缠熵（$ osee $）的传播是为了探索平衡外量子多体系统的关键。在这里，我们认为，对于综合模型，$ osee $的动力学与基础准颗粒的扩散有关。我们得出了一些简单的$ OSEE $，即低级别的对角线本地运营商的$ OSEE $。我们从数值上检查了界限是否在规则$ 54 $链中饱和，该规则代表了交互的集成系统。值得注意的是，在旋转1/2 heisenberg $ xxz $链中相同的界限饱和。 $ OSEE $远离各向同性点和自由屈服点，无论链条各向异性如何，$ osee $都将其增长为$ 1/2 \ ln（t）$，表明普遍性。最后，我们讨论了可集成性破坏的效果。我们表明存在强大的有限时间效果，这阻止了$ osee $的渐近行为。
Understanding the spreading of the operator space entanglement entropy ($OSEE$) is key in order to explore out-of-equilibrium quantum many-body systems. Here we argue that for integrable models the dynamics of the $OSEE$ is related to the diffusion of the underlying quasiparticles. We derive the logarithmic bound $1/2\ln(t)$ for the $OSEE$ of some simple, i.e., low-rank, diagonal local operators. We numerically check that the bound is saturated in the rule $54$ chain, which is representative of interacting integrable systems. Remarkably, the same bound is saturated in the spin-1/2 Heisenberg $XXZ$ chain. Away from the isotropic point and from the free-fermion point, the $OSEE$ grows as $1/2\ln(t)$, irrespective of the chain anisotropy, suggesting universality. Finally, we discuss the effect of integrability breaking. We show that strong finite-time effects are present, which prevent from probing the asymptotic behavior of the $OSEE$.
