We gauge the fermion parity symmetry of the Kitaev chain. While the bulk of the model becomes an Ising chain of gauge-invariant spins in a tilted field, near the boundaries the global fermion parity symmetry survives gauging, leading to local gauge-invariant Majorana operators. In the absence of vortices, the Higgs phase exhibits fermionic symmetry-protected topological (SPT) order distinct from the Kitaev chain. Moreover, the deconfined phase can be stable even in the presence of vortices. We also undertake a comprehensive study of a gently gauged model which interpolates between the ordinary and gauged Kitaev chains. This showcases rich quantum criticality and illuminates the topological nature of the Higgs phase. Even in the absence of superconducting terms, gauging leads to an SPT phase which is intrinsically gapless due to an emergent anomaly.

中文翻译：

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测量 Kitaev 链

我们测量了 Kitaev 链的费米子奇偶对称性。虽然模型的大部分变成了倾斜场中规范不变自旋的 Ising 链，但在边界附近，全局费米子奇偶对称性在规范中仍然存在，导致局部规范不变的 Majorana 算子。在没有涡流的情况下，希格斯相表现出与 Kitaev 链不同的费米子对称保护拓扑 (SPT) 顺序。此外，即使在存在涡流的情况下，去约束相也可以是稳定的。我们还对在普通和测量的 Kitaev 链之间插值的温和测量模型进行了全面研究。这展示了丰富的量子临界性并阐明了希格斯相的拓扑性质。即使没有超导项，测量也会导致 SPT 相位，由于出现异常，该相位本质上是无间隙的。