论文标题
本质上无间隙的拓扑阶段
Intrinsically Gapless Topological Phases
论文作者
论文摘要
量子物质中的拓扑通常与间隙阶段有关。例如,在对称受保护的拓扑(SPT)阶段中,大量能量差距将边界附近的边缘模式定位。在这项工作中,我们确定了一种新的机制,该机制导致拓扑阶段不仅是无间隙,而且缺乏间隙是必不可少的。这些“本质上无间隙的SPT阶段”没有间隙的对应物,因此与最近发现的无间隙SPT相的例子不同。这些阶段的基本要素是,现场对称性在低能方面以异常方式起作用。发现本质上的无间隙SPT阶段显示出几种独特的属性,包括(i)受保护的边缘模式,这些模式在具有相同对称性的间隙系统中无法实现,(ii)弦顺序参数,这些参数在间隙阶段中同样被禁止,并且(iii)在扰动相位时获得的相图受到的约束。我们使用数值模拟和有效的场理论,在受$ \ mathbb z_4 $对称性保护的特定实现中验证了对一般理论的预测。我们还讨论了更高维度和可能的实验实现的扩展。
Topology in quantum matter is typically associated with gapped phases. For example, in symmetry protected topological (SPT) phases, the bulk energy gap localizes edge modes near the boundary. In this work we identify a new mechanism that leads to topological phases which are not only gapless but where the absence of a gap is essential. These `intrinsically gapless SPT phases' have no gapped counterpart and are hence also distinct from recently discovered examples of gapless SPT phases. The essential ingredient of these phases is that on-site symmetries act in an anomalous fashion at low energies. Intrinsically gapless SPT phases are found to display several unique properties including (i) protected edge modes that are impossible to realize in a gapped system with the same symmetries, (ii) string order parameters that are likewise forbidden in gapped phases, and (iii) constraints on the phase diagram obtained upon perturbing the phase. We verify predictions of the general theory in a specific realization protected by $\mathbb Z_4$ symmetry, the one dimensional Ising-Hubbard chain, using both numerical simulations and effective field theory. We also discuss extensions to higher dimensions and possible experimental realizations.