论文标题
量子液体的普遍纠缠签名作为费米子临界的指南
Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
论文作者
论文摘要
一个杰出的挑战涉及了解相互作用系统中出现的量子物质液态的多个粒子纠缠。 $ d $空间维度中的费米液体（FL）显示了一个在真实空间纠缠中的区域法（长度$ l $），$ s_ {ee} \ sim l^{d-1} \ ln l $，被认为是互动量不相互作用的固定系统的基础标志。在这项工作中，我们将$ t = 0 $ renoralatianation Group方法应用于动量（或$ k $）的FL原型 - 空间，从而揭示了RG相关的量子波动（由于向前和切向散射），从而产生了远距离的纠缠。对非纤维化液体（例如2D边缘费米液体（MFL）和1d tomonaga-luttinger液体（TLL））的类似分析表明，在$ k $ -space窗口中定义的子系统定义的子系统中的无间隙电子液体中的区域law的普遍性违反了$ k $ - $ usizations of size $λ$λ$λ$λ$λ$λ$λ，并且费米表面。我们将这种分析扩展到由于反向散射过程引起的量子波动而导致费米表面不稳定的量子液体。确实，我们发现，$ k $空间的纠缠符号的符号似乎受其出现的费米表面的性质（例如，是否嵌套）的性质，以及其父母无间隙金属液体的性质（例如，FL，MFL等）。我们的发现，在最佳孔掺杂时，我们发现在2D哈伯德模型中发现的量子临界点上存在的节点MFL的增强的纠缠熵证实了这一点。因此，我们的工作为基于纠缠的量子液体的分类铺平了道路，从相互作用的费米子物质的关键性中出现。
An outstanding challenge involves understanding the many-particle entanglement of liquid states of quantum matter that arise in systems of interacting electrons. The Fermi liquid (FL) in $D$ spatial dimensions shows a violation of the area-law in real-space entanglement entropy of a subsystem (of length $L$), $S_{EE} \sim L^{D-1}\ln L$, widely believed to be a hallmark signature of the ground state of a gapless quantum critical system of interacting fermions. In this work, we apply a $T=0$ renormalisation group approach to a prototype of the FL in momentum (or, $k$)-space, unveiling thereby the RG relevant quantum fluctuations (due to forward and tangential scattering) from which long-range entanglement arises. A similar analysis of non-Fermi liquids such as the 2D marginal Fermi liquid (MFL) and the 1D Tomonaga-Luttinger liquid (TLL) reveals a universal logarithmic violation of the area-law in gapless electronic liquids for a subsystem defined within a $k$-space window (of size $Λ$) proximate to the Fermi surface, with a proportionality constant that depends on the nature of the underlying Fermi surface. We extend this analysis to the gapped quantum liquids emergent from the destabilisation of the Fermi surface by quantum fluctuations arising from backscattering processes. Indeed, we find that the $k$-space entanglement signatures of gapped quantum liquids appear to be governed by the nature of the Fermi surface (e.g., nested or not) from which they emerge, as well as the nature of their parent gapless metallic liquid (e.g., FL, MFL etc.). This is confirmed by our finding an enhanced entanglement entropy for the nodal MFL present at the quantum critical point recently discovered in the 2D Hubbard model at optimal hole-doping. Our work thus paves the way for an entanglement based classification of quantum liquids emergent from the criticality of interacting fermionic matter.
