Time Evolution of Entanglement Entropy on Quenches of Inhomogenous Quantum Systems

Abstract

The purpose of this paper is to study the properties of entanglement entropy after a quantum quench from the uniform Hamiltonian into an Inhomogenous Hamiltonian. I will first review the setting of our quenches, which is a Conformal Field Theory. Next, I will explain entanglement entropy, its importance, and how it can be calculated using correlations of twist operators. Next, I will explain various methods which exist to study entanglement entropy in the context of the Mobius Transformation. One method will involve a coordinate transformation on the metric, one will involve quasiparticles and their trajectories, and the last will involve a coordinate transformation on the boundaries of the subsystem. The correspondance between the two main methods, the change of metric method and the change of boundary method, will be proven. Next, three other inhomogenous systems will be introduced, known as the Entanglement, Rindler, and Rainbow Chain deformations, and studied using these methods. New physics can be seen on the semi-infinite line, where finite boundaries will result in behavior which has not been studied.