Department of Physics, University of Florida, Gainesville, Florida 32611-8440, USA.
Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77a, 50937 Köln, Germany.
Phys Rev Lett. 2018 Oct 5;121(14):147602. doi: 10.1103/PhysRevLett.121.147602.
The numerical renormalization group is used to study quantum entanglement in the Kondo impurity model with a density of states ρ(ϵ)∝|ϵ|^{r} (0<r<1/2) that vanishes at the Fermi energy ϵ=0. This nonintegrable model features a Kondo-destruction quantum critical point (QCP) separating a partially screened phase from a local-moment phase. The impurity contribution S_{e}^{imp} to the entanglement entropy between a region of radius R around the magnetic impurity and the rest of the system reveals a length scale R^{} that distinguishes a region R≪R^{} of strong critical entanglement from one R≫R^{} of weak entanglement. Within each phase, S_{e}^{imp} is a universal function of R/R^{} with a power-law decay for R/R^{}≫1. The entanglement length R^{} diverges on approach to the interacting QCP, showing that the critical Kondo screening cloud subsumes the entire system as the impurity becomes maximally entangled with the conduction band. This work has implications for entanglement calculations in other models and for the nature of heavy-fermion quantum criticality.
数值重整化群被用来研究具有态密度 ρ(ϵ)∝|ϵ|^{r} (0<r<1/2) 的 Kondo 杂质模型中的量子纠缠，其中 ρ(ϵ) 在费米能 ϵ=0 处为零。这个不可积模型具有 Kondo 破坏量子临界点 (QCP)，将部分屏蔽相和局域磁矩相分开。磁性杂质周围半径为 R 的区域与系统其余部分之间的纠缠熵的杂质贡献 S_{e}^{imp} 揭示了一个区分强临界纠缠区域 R≪R^{} 和弱纠缠区域 R≫R^{} 的长度尺度 R^{}。在每个相中，S_{e}^{imp} 是 R/R^{} 的通用函数，对于 R/R^{}≫1 具有幂律衰减。纠缠长度 R^{} 在接近相互作用 QCP 时发散，表明当杂质与导带最大纠缠时，临界 Kondo 屏蔽云包含整个系统。这项工作对其他模型中的纠缠计算以及重费米子量子临界点的性质都有影响。
