AI 中文总结
该研究针对Tomonaga-Luttinger液体的投影系综，通过Replica边界共形场论和数值计算，揭示了其通用非线性态重叠矩层级及与Luttinger参数无关的主导标度指数，明确了几何起源并获数值验证。
AI 中文摘要
局域测量将多体波函数转化为条件量子态的统计系综。在混沌系统中，此类系综的高阶矩可诊断量子态随机性的出现，但其在平衡量子临界性下的结构在很大程度上未知。本文表明，Tomonaga-Luttinger液体的投影系综呈现出通用的非线性态重叠矩层级；值得注意的是，主导标度指数与连续变化的Luttinger参数无关。Replica边界共形场论揭示了其几何起源：结果锁定将主动的replica交换合并为单一的集体旋转扇区，而相交的紧致replica膜消除了主导的依赖相互作用的零模贡献。对相互作用XXZ临界相的矩阵乘积态计算以及直接自由费米子计算均独立证实了该相互作用无关性与非线性层级。
英文摘要
Local measurements transform a many body wavefunction into a statistical ensemble of conditional quantum states. In chaotic systems, the higher moments of such ensembles diagnose the emergence of quantum state randomness, but their structure at equilibrium quantum criticality is largely unknown. Here we show that the projected ensemble of a Tomonaga-Luttinger liquid exhibits a universal nonlinear hierarchy of state overlap moments. Remarkably, the leading scaling exponents are independent of the continuously varying Luttinger parameter. Replica boundary conformal field theory reveals a geometric origin: outcome locking combines the active replica swaps into a single collective rotated sector, while intersecting compact replica branes eliminate the leading interaction dependent zero mode contribution. Matrix product state calculations across the interacting XXZ critical phase and direct free fermion calculations independently confirm the interaction independence and nonlinear hierarchy.
Comments6+10 pages, 3 figures
