Exploring Relations Between Symmetry-Protected Topological Phases and Long-Range Entangled Phases

In this seminar, we will discuss an explicit relation between symmetry-protected topological (SPT) phases and long-range entangled states. Starting with an overview of SPT phases, we will explore the 1+1 d lattice ZXZ model as a key example. The discussion will then shift to the toric code model in 2+1 dimensions, which is a pivotal example of a topologically-ordered system. We will discuss a procedure that allows us to obtain topological order from the symmetry of SPTs and provide an explicit example by constructing the toric code model from copies of ZXZ chains