论文标题
放松的费米子SPT阶段：超对称扩展
Unwinding Fermionic SPT Phases: Supersymmetry Extension
论文作者
论文摘要
我们展示了1+1维效率对称性保护的拓扑状态（SPT，即，非平凡的短距离纠缠纠缠的量子物质阶段，其边界表现出hooft异常表现出hooft异常，其体积不能使其在有限的量化范围内的繁琐量量的整体变化中逐渐变形，而在整体中，在整体上是在整体中的繁琐量，并且在整体上都可以在整体上进行一定的能力，并且在整体上是一定能力的，就可以在整体上占有一致的能力，并且在整体上是一定的，它的范围是一定的，它的范围是一定的，它的范围是一定的。希尔伯特（Hilbert）空间通过增加自由度，并适当地扩展全球对称性。边界上的扩展投影全局对称性可以从特定意义上变为超对称性，即，它包含与费米昂数字奇偶校验$（-1）^f $上下班的组元素，而反自然的时间转换对称性则被分数化。这也意味着我们可以通过适当的超对称性扩展来提高和删除某些异国情调的效率异常（例如，时间反转或反射对称性的“奇偶校验”异常）。我们为1+1d Majorana fermion链的多层构成明确的例子，然后对Sachdev-Ye-Kitaev（Syk）相互作用，由Supersymmemaly保护的固有的Fermionic无间隙SPT进行评论，并通过协调理论对更高的空间尺寸进行概括。
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.
