论文标题
在一维本质上无间隙拓扑阶段的纠缠熵轮廓中没有弗里德尔振荡
Absence of Friedel oscillations in the entanglement entropy profile of one-dimensional intrinsically gapless topological phases
论文作者
论文摘要
拓扑量子物质通常与散装间隙保护的间隙相和边缘模式有关。相反，最近的工作（Phys。V.B 104，075132）提出了本质上无间隙的拓扑阶段，在一个维度上，只有当散装是无间隙的Luttinger液体时，才具有保护边缘模式。这种拓扑luttinger液体（TLL）的边缘模式来自非局部弦顺序，该弦顺序被禁止在间隙阶段中，其精确形式取决于系统的对称类别。在这项工作中，我们提出了一个强大的，公正的基于纠缠的吸烟枪的签名。特别是，我们表明，TLL的纠缠熵剖面缺乏弗里德尔振荡，这些振荡总是存在于其他无间隙的一维相等于普通的luttinger液体中，并认为它们的缺失与长期范围的弦乐顺序密切相关，这是TLL的内在特性。至关重要的是，这种诊断对数值误差的稳健性和在实验中的测量相对较容易，因为它依赖于纠缠熵而不是纠缠频谱，这与基于纠缠的基于纠缠的拓扑阶段的诊断范围在一个维度上不同。
Topological quantum matter is typically associated with gapped phases and edge modes protected by the bulk gap. In contrast, recent work (Phys. Rev. B 104, 075132) proposed intrinsically gapless topological phases that, in one dimension, carry protected edge modes only when the bulk is a gapless Luttinger liquid. The edge modes of such a topological Luttinger liquid (TLL) descend from a nonlocal string order that is forbidden in gapped phases and whose precise form depends on the symmetry class of the system. In this work, we propose a powerful and unbiased entanglement-based smoking gun signature of the TLL. In particular, we show that the entanglement entropy profile of a TLL lacks Friedel oscillations that are invariably present in other gapless one dimensional phases such as ordinary Luttinger liquids, and argue that their absence is closely related to a long-ranged string order which is an intrinsic property of the TLL. Crucially, such a diagnostic is more robust against numerical errors and relatively easier to measure in experiments as it relies on the entanglement entropy rather than entanglement spectrum, unlike the entanglement-based diagnostics of gapped topological phases in one dimension.
