Intrinsically gapless topological phases
Intrinsically gapless topological phases
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DOI：
10.1103/physrevb.104.075132
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发表时间：
2020-08
影响因子：
3.7
通讯作者：
Ryan Thorngren;A. Vishwanath;R. Verresen
中科院分区：
文献类型：
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作者：
Ryan Thorngren;A. Vishwanath;R. Verresen
量子物质的拓扑结构通常与间隙相有关。例如，在对称保护拓扑（SPT）相中，块能隙使边界附近的边缘模式局部化。在这项工作中，我们确定了一种新的机制，这种机制导致拓扑相不仅是无间隙的，而且没有间隙是必不可少的。这些“本质上无间隙的SPT相”没有间隙对应物，因此也与最近发现的无间隙SPT相的例子不同。这些相的基本成分是，在低能量下，现场对称性以反常的方式起作用。本质上无间隙的SPT相显示出几个独特的特性，包括(i)在具有相同对称性的间隙系统中不可能实现的保护边缘模式，（ii）在间隙相中同样禁止的弦序参数，以及（iii）在相位扰动时获得的相图的约束。我们用数值模拟和有效场论两种方法，验证了一般理论在一维伊辛-哈伯德链($\mathbb Z_4$对称性保护下的具体实现中的预测。我们还讨论了向更高维度的扩展和可能的实验实现。
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.