对称扭曲多熵：二维SPT相的序参量
Symmetry-Twisted Multi-Entropies: Order Parameters for 2D SPT Phases
AI总结：
研究如何从期望值提取二维玻色SPT信息，提出基于部分对称和置换操作期望值的非局部序参量，对应对称扭曲多熵，能检测四体和六体纠缠，限制虚假贡献，有望推广到费米子和高维系统。
AI中文摘要：
尽管对称保护拓扑相（SPTs）可通过其纠缠特性区分，但在一维情况之外，如何直接从期望值中提取此信息尚不清楚。本文填补了这一空白，提出了一对非局部序参量，可检测和区分二维中受内部离散阿贝尔酉对称保护的所有玻色SPT。通过在拓扑非平凡时空流形上有效模拟SPT路径积分，这些量可提取所需拓扑不变量。序参量根据作用于有限空间区域中系统固定数量副本的部分对称和置换操作的期望值定义，这些期望值对应于被称为多熵的多体纠缠量的对称扭曲版本。明确表明两个序参量分别检测对称保护的四体和六体纠缠，并限制了可能的“虚假”贡献。在定点晶格模型中进行了分析测试。结果表明多体纠缠是SPT的一个决定性特征；确实期望这些方法能推广到费米子和更高维系统。
英文摘要：
Although symmetry-protected topological phases (SPTs) can be distinguished by their entanglement properties, it has been unclear how to extract this information directly from expectation values beyond the 1D case. Here, we close this gap and propose a pair of nonlocal order parameters that can detect and distinguish all bosonic SPTs in 2D protected by internal discrete, Abelian unitary symmetries. The desired topological invariants are extracted by these quantities by effectively simulating the SPT path integral on topologically non-trivial spacetime manifolds. Our order parameters are defined in terms of expectation values of partial symmetry and permutation operations acting on fixed numbers of replicas of the system in finite spatial regions. These expectation values correspond to symmetry-twisted versions of multipartite entanglement quantities known as multi-entropies. We show explicitly that our two order parameters detect symmetry-protected four-party and six-party entanglement, respectively, and we constrain possible "spurious" contributions. We analytically test our proposal in fixed-point lattice models. Our results suggest multipartite entanglement to be a defining feature of SPTs; indeed, we expect our methods to generalize to fermionic and higher-dimensional systems.
