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，纠缠的定量度量，如基态的纠缠熵，除了在最简单的系统中，很难计算。超对称理论（SUSY）著名的承认观察，如维滕指数，这是不变的超对称保持变形，并可以计算本地化。它们还经常表现出大的简并性和伴随的零能量（或更一般的超对称性保持）基态的希尔伯特空间。在这个项目中，我们将试图制定和计算观测量，测量纠缠的状态在这个子空间。

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.