Protected Observables in Supersymmetric Theories as a Probe of Entanglement

纠缠的研究在理解量子多体系统中起着核心作用。然而，除了在最简单的系统中，测量纠缠的定量措施，如基态的纠缠熵是很难计算的。超对称理论(SUSY)著名地承认Witten指数等可观测量在SUSY保持形变下是不变的，并且可以通过局部化来计算。它们还经常表现出大的简并和伴随的零能量(或者更一般的超对称保持)基态的希尔伯特空间。在这个项目中，我们将尝试建立和计算在这个子空间中测量状态纠缠的可观测数据。

The study of entanglement plays a central role in understanding quantum many body systems. However, quantitative measures of entanglement such as the entanglement entropy of the groundstate are hard to compute except in the simplest systems. Supersymmetric theories (SUSY) famously admit observables such as the Witten index which are invariant under SUSY preserving deformations and can be computed by localisation. They also often exhibit large degeneracies and an accompanying Hilbert space of zero energy (or more generally SUSY preserving) groundstates. In this project we will attempt to formulate and compute observables which measure the entanglement of states in this subspace.