Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
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DOI：
10.1103/physrevb.98.220303
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发表时间：
2018-12-17
影响因子：
3.7
通讯作者：
Vasseur, Romain
中科院分区：
文献类型：
--
作者：
Gopalakrishnan, Sarang;Huse, David A.;Vasseur, Romain
我们讨论了相互作用的可积格模型中算子扩散的流体动力学问题。在这些模型中，算符通过准粒子的弹道传播进行传播，算符前沿的速度由最快的准粒子速度局部设定。在相互作用的可积系统中，这一速度依赖于其他准粒子的密度，因此平衡密度涨落导致前锋遵循有偏的随机行走，从而扩散扩大。弹道波阵面传播和扩散波阵面展宽在一维不可积系统中也普遍存在；因此，尽管在这两种情况下算子扩散的机制是不同的，但这些算子阵面的粗粒度度量不能区分这两种情况。我们给出了波前展宽率的一个表达式；对于一个特殊的可积模型(“Floquet-Fredrickson-Andersen”模型)，我们明确地推导出了它的表达式，并从动力学的角度论证了它应该普遍适用。我们的结果阐明了相互作用可积模型中弹道输运扩散修正的微观机制。
We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the fastest quasiparticle velocity. In interacting integrable systems, this velocity depends on the density of the other quasiparticles, so equilibrium density fluctuations cause the front to follow a biased random walk, and therefore to broaden diffusively. Ballistic front propagation and diffusive front broadening are also generically present in nonintegrable systems in one dimension; thus, although the mechanisms for operator spreading are distinct in the two cases, these coarse-grained measures of the operator front do not distinguish between the two cases. We present an expression for the front-broadening rate; we explicitly derive this for a particular integrable model (the "Floquet-Fredrickson-Andersen" model), and argue on kinetic grounds that it should apply generally. Our results elucidate the microscopic mechanism for diffusive corrections to ballistic transport in interacting integrable models.