费米子SPT相的解绕：超对称性的扩展
Unwinding Fermionic SPT Phases: Supersymmetry Extension
摘要：
我们证明了1+1维费米子保序拓扑态（SPT，即量子物质的非平凡短程纠缠带隙相，其边界表现出t Hooft异常，并且其体积仅在存在全局对称性的情况下在有限深度局部幺正变换下不能变形为平凡张量积态），实际上，通过增加额外的自由度和适当地扩展全局对称性来扩大希尔伯特空间，可以将其解绕到平凡状态。边界上的扩展射影全局对称性可以在特定意义上成为超对称的，即，它包含不与费米子数奇偶性$(-1)^F$交换的群元素，而反酉时间反演对称性变得分数化。这也意味着我们可以提升和移除某些奇异的费米异常（例如，时间反演或反射对称中的“宇称”异常）通过群扩展方面的适当超对称扩展。我们制定了明确的1+1d马约拉纳费米子链的多层的例子，然后评论模型与Sachdev-Ye-Kitaev（SYK）的相互作用，内在的费米子无隙的SPT保护超对称性，并通过协边理论推广到更高的时空维度。
英文摘要：
We show how 1+1-dimensional fermionic symmetry-protected topological states (SPTs, i.e. nontrivial short-range entangled gapped phases of quantum matter whose boundary exhibits 't Hooft anomaly and whose bulk cannot be deformed into a trivial tensor product state under finite-depth local unitary transformations only in the presence of global symmetries), indeed can be unwound to a trivial state by enlarging the Hilbert space via adding extra degrees of freedom and suitably extending the global symmetries. The extended projective global symmetry on the boundary can become supersymmetric in a specific sense, i.e., it contains group elements that do not commute with the fermion number parity $(-1)^F$, while the anti-unitary time-reversal symmetry becomes fractionalized. This also means we can uplift and remove certain exotic fermionic anomalies (e.g., "parity" anomaly in time-reversal or reflection symmetry) via appropriate supersymmetry extensions in terms of group extensions. We work out explicit examples for multi-layers of 1+1d Majorana fermion chains, then comment on models with Sachdev-Ye-Kitaev (SYK) interactions, intrinsic fermionic gapless SPTs protected by supersymmetry, and generalizations to higher spacetime dimensions via a cobordism theory.
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