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，纠缠的定量测量，如基态的纠缠熵，很难计算，除非在最简单的系统。众所周知，超对称理论（SUSY）承认像Witten指数这样的可观测值在保持SUSY的变形下是不变的，并且可以通过局部化来计算。它们也经常表现出大的简并和伴随的零能量（或更普遍地保持超对称性）基态的希尔伯特空间。在这个项目中，我们将尝试制定和计算测量该子空间中状态纠缠的可观测值。

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.