论文标题
特征态纠缠缩放，以进行关键相互作用旋转链
Eigenstate entanglement scaling for critical interacting spin chains
论文作者
论文摘要
随着子系统的大小和能量的增加，能量本征态的两分纠缠熵从地面尺度延伸到体积定律。在先前的工作中，我们指出，当应用强或弱的特征态热化（ETH）时，几乎所有本征态的纠缠熵分别遵循一个单一的交叉函数。交叉函数由热状态的子系统熵确定，并在量子临界方案中采用通用缩放形式。这是通过现场理论论证以及对非相互作用的费米和玻色子的大型系统的分析所证明的。在这里，我们使用精确的对角线化来证实这种缩放特性，用于在临界点处的可集成和不可集成的相互作用的自旋1/2链。特别是，我们分析了有和没有下一步最邻居相互作用的XXZ和横向视野模型。实际上，可以通过共形场理论的通用缩放函数来描述热子系统熵的交叉。此外，我们在这些模型中分析了ETH对纠缠的有效性。即使对于可以模拟的相对较小的系统尺寸，本征态纠缠熵的分布也会在相应的热合体的子系统熵周围峰值达到峰值。
With increasing subsystem size and energy, bipartite entanglement entropies of energy eigenstates cross over from the groundstate scaling to a volume law. In previous work, we pointed out that, when strong or weak eigenstate thermalization (ETH) applies, the entanglement entropies of all or, respectively, almost all eigenstates follow a single crossover function. The crossover functions are determined by the subsystem entropy of thermal states and assume universal scaling forms in quantum-critical regimes. This was demonstrated by field-theoretical arguments and the analysis of large systems of non-interacting fermions and bosons. Here, we substantiate such scaling properties for integrable and non-integrable interacting spin-1/2 chains at criticality using exact diagonalization. In particular, we analyze XXZ and transverse-field Ising models with and without next-nearest-neighbor interactions. Indeed, the crossover of thermal subsystem entropies can be described by a universal scaling function following from conformal field theory. Furthermore, we analyze the validity of ETH for entanglement in these models. Even for the relatively small system sizes that can be simulated, the distributions of eigenstate entanglement entropies are sharply peaked around the subsystem entropies of the corresponding thermal ensembles.
