随机分形晶格上自由费米子的纠缠熵
Entanglement Entropy of Free Fermions on Random Fractal Lattices
中文总结 AI 辅助
研究随机分形晶格上自由费米子的纠缠特性，通过随机增长算法生成晶格并调整维度，计算不同填充基态的纠缠熵及标度关系，研究全局猝灭后的纠缠增长，揭示仅几何随机性就能产生非平凡纠缠结构和缓慢量子信息传播。
中文摘要 AI 辅助
随机分形晶格提供了一种几何无序的环境，其中量子关联可由非整数维而非局域随机性塑造。我们研究了通过随机增长算法生成的随机分形晶格上非相互作用费米子的纠缠特性。通过改变增长参数并以概率\(p\)添加缺失链接来调整豪斯多夫维和谱维，同时保持系统无局域无序。对于不同填充的基态，计算由图距离定义的子区域的二分纠缠熵并分析其与子系统大小的标度关系。在广泛参数范围内发现主要由豪斯多夫维主导的稳健幂律行为，符合广义面积定律且无欧几里得自由费米子中常见的对数增强。还研究了从不相关棋盘态全局猝灭后的纠缠增长，发现渐近标度塌缩，子系统大小依赖由豪斯多夫维主导，时间演化由谱维主导，动力学在扩展中间时间窗口内对数缓慢。这些结果表明仅几何随机性就能在自由费米子系统中产生非平凡基态纠缠结构和缓慢量子信息传播。
英文摘要
Random fractal lattices provide a geometrically disordered setting in which quantum correlations can be shaped by noninteger dimensionality rather than onsite randomness. We investigate the entanglement properties of noninteracting fermions on random fractal lattices generated by a stochastic growth algorithm. By varying the growth parameter and adding missing links with probability $p$, we tune the Hausdorff and spectral dimensions while keeping the system free of onsite disorder. For ground states at different fillings, we compute the bipartite entanglement entropy of subregions defined by graph distance and analyze its scaling with subsystem size. Over a broad parameter range, we find robust power-law behavior governed primarily by the Hausdorff dimension, consistent with a generalized area law and without the logarithmic enhancement familiar from Euclidean free fermions. We also study entanglement growth following a global quench from an uncorrelated checkerboard state and uncover an asymptotic scaling collapse in which the subsystem-size dependence is governed by the Hausdorff dimension, while the temporal evolution is governed by the spectral dimension. The resulting dynamics are logarithmically slow over an extended intermediate-time window. These results show that geometric randomness alone can generate both nontrivial ground-state entanglement structure and slow quantum-information spreading in free-fermion systems.
