AI 中文总结
该研究证实量子杂质模型的能量空间纠缠具有普适性，揭示其与一维拓扑能带理论的关联，还通过两轨道安德森模型的相变验证了费米液体与非费米液体区的纠缠行为规律。
AI 中文摘要
纠缠熵（EE）通常通过实空间二分法进行研究。我们证明，在量子杂质模型中，等价于浴的动量空间二分法的能量空间二分法可呈现普适行为。受穷人数标度（poor man's scaling）的启发，我们对浴进行对数离散化并将其划分为高能和低能区域。对于具有费米液体不动点的模型，包括安德森模型以及完全屏蔽或欠屏蔽的近藤模型，低能EE会流向与模型参数无关的常数。这些常数是ln2的整数倍加上仅依赖于对数离散化参数Λ的修正项。我们证明，能量空间中不动点波函数的标度不变性映射到一维链上的有效平移不变性，使得这些不动点可通过一维拓扑能带理论进行分类。在低能手征对称性下，每个ln2的贡献源自拓扑边缘模式。我们还利用两轨道安德森模型中由轨道间反铁磁耦合驱动的局域单重态-近藤单重态转变，研究不同费米液体不动点之间的跃迁。局域单重态相具有有效解耦的杂质和几乎消失的EE，而近藤单重态相的有限EE大于每自旋和每轨道一个ln2。当低能下手征对称性成立时，这种区别对应于有效浴链的拓扑跃迁。在非费米液体临界点，EE形成不稳定平台，其Λ依赖性类似于过屏蔽两通道近藤模型的情况，支持同一非费米液体普适类内的普适性。
英文摘要
Entanglement entropy (EE) is commonly studied using real-space bipartitions. We show that, in quantum impurity models, an energy-space bipartition, equivalent to the momentum-space bipartition of the bath, can display universal behavior. Motivated by poor man's scaling, we logarithmically discretize the bath and partition it into high- and low-energy sectors. For models with Fermi-liquid fixed points, including the Anderson model and fully screened or underscreened Kondo models, the low-energy EE flows to constants independent of model parameters. These constants are integer multiples of $\ln 2$ plus corrections that depend only on the logarithmic discretization parameter $Λ$. We show that scale invariance of the fixed-point wavefunction in energy space maps to effective translation invariance along a one-dimensional chain, allowing the fixed points to be classified by one-dimensional topological band theory. With low-energy chiral symmetry, each $\ln 2$ contribution originates from a topological edge mode. We also study transitions between distinct Fermi-liquid fixed points using the local-singlet--Kondo-singlet transition in a two-orbital Anderson model driven by an inter-orbital antiferromagnetic coupling. The local-singlet phase has an effectively decoupled impurity and nearly vanishing EE, whereas the Kondo-singlet phase has finite EE larger than $\ln 2$ per spin and orbital. When chiral symmetry holds at low energies, this distinction corresponds to a topological transition of the effective bath chain. At the non-Fermi-liquid critical point, the EE develops an unstable plateau. Its $Λ$ dependence resembles that of the overscreened two-channel Kondo model, supporting universality within the same non-Fermi-liquid universality class.
Comments7+17 pages, 4+4 figures
