论文标题
费米液体中的拓扑多部分纠缠
Topological Multipartite Entanglement in a Fermi Liquid
论文作者
论文摘要
我们表明，费米海的拓扑是$ d $维费米气体的拓扑，反映在一定程度上相遇的$ d+1 $区域的多方纠缠中。对于奇数$ d $，我们介绍了多部分共同信息，并表明它表现出$ \ log^d l $ divergence作为系统尺寸$ l $的函数，其通用系数与Fermi Sea的Euler特性$χ_f$成正比。这为费米气体提供了一个概括，即$ d = 1 $的众所周知结果，该结果表达了$ \ log l $ d $ divergence the Contrange $ c $ c $表征保形场理论的$ \ log l $差异。对于$ d $，我们引入了一个充电加权纠缠熵，在粒子孔转换下显然是奇怪的。我们表明，相应的充电加权互信息表现出类似的$ \ log^d l $ divergence与$χ_f$成比例。我们的分析将多部分相互信息的普遍行为与$ d+1 $'第相等密度相关函数相同的情况下，我们表明的是，在长波长极限上表现出了普遍的行为，与$χ_f$成比例。我们的分析结果基于复制方法。此外，我们对$ d = 2 $的电荷加权互信息进行了数值研究，该信息证实了分析理论的几个方面。最后，我们在副本理论中考虑相互作用的效果。我们表明，对于$ d = 3 $，$ \ log^3 l $ dovergence的拓扑共同信息不会受到弱的短距离互动的扰动，尽管对于$ d = 2 $，收费加权的共同信息会受到干扰。因此，对于$ d = 3 $，多部分共同信息提供了一个可靠的分类，可以区分不同的拓扑费米液相。
We show that the topology of the Fermi sea of a $D$-dimensional Fermi gas is reflected in the multipartite entanglement characterizing $D+1$ regions that meet at a point. For odd $D$ we introduce the multipartite mutual information, and show that it exhibits a $\log^D L$ divergence as a function of system size $L$ with a universal coefficient that is proportional to the Euler characteristic $χ_F$ of the Fermi sea. This provides a generalization, for a Fermi gas, of the well-known result for $D=1$ that expresses the $\log L$ divergence of the bipartite entanglement entropy in terms of the central charge $c$ characterizing a conformal field theory. For even $D$ we introduce a charge-weighted entanglement entropy that is manifestly odd under a particle-hole transformation. We show that the corresponding charge-weighted mutual information exhibits a similar $\log^D L$ divergence proportional to $χ_F$. Our analysis relates the universal behavior of the multipartite mutual information in the absence of interactions to the $D+1$'th order equal-time density correlation function, which we show exhibits a universal behavior in the long wavelength limit proportional to $χ_F$. Our analytic results are based on the replica method. In addition we perform a numerical study of the charge-weighted mutual information for $D=2$ that confirms several aspects of the analytic theory. Finally, we consider the effect of interactions perturbatively within the replica theory. We show that for $D=3$ the $\log^3 L$ divergence of the topological mutual information is not perturbed by weak short-ranged interactions, though for $D=2$ the charge-weighted mutual information is perturbed. Thus, for $D=3$ the multipartite mutual information provides a robust classification that distinguishes distinct topological Fermi liquid phases.
