标题： 真实多熵，二面体不变量和利夫希茨理论 显示英文标题

标题： Genuine multi-entropy, dihedral invariants and Lifshitz theory

摘要： 多不变量是状态副本的局部酉不变量，作为研究量子多体系统中多体纠缠和关联的潜在新探针而被提出。 在本文中，我们研究了三部分纯态的两个多不变量，即多熵和二面体不变量。 我们计算了Lifshitz理论基态的（真实）多熵，并获得了其到非整数Rényi指数的解析延拓。 我们证明，真实多熵可以用互信息和对数否定性来表示。 对于一般的三部分纯态，我们证明二面体不变量直接与Rényi反射熵相关。 特别是，我们证明了副本的二面体排列等价于反射构造，或者等价于密度矩阵的重新排列。 显示英文摘要

摘要： Multi-invariants are local unitary invariants of state replicas introduced as potential new probes of multipartite entanglement and correlations in quantum many-body systems. In this paper, we investigate two multi-invariants for tripartite pure states, namely multi-entropy and dihedral invariant. We compute the (genuine) multi-entropy for groundstates of Lifshitz theories, and obtain its analytical continuation to noninteger values of R\'enyi index. We show that the genuine multi-entropy can be expressed in terms of mutual information and logarithmic negativity. For general tripartite pure states, we demonstrate that dihedral invariants are directly related to R\'enyi reflected entropies. In particular, we show that the dihedral permutations of replicas are equivalent to the reflected construction, or alternatively to the realignment of density matrices.