Entanglement entropy after selective measurements in quantum chains

TL;DR

This paper investigates the behavior of bipartite entanglement entropy after selective measurements in quantum chains, connecting it to conformal field theory, Casimir energy, and providing formulas for various system configurations.

Contribution

It introduces a comprehensive analysis of post measurement entanglement entropy in critical and massive quantum systems, including new formulas and a method for free fermion systems.

Findings

Entanglement entropy relates to Casimir energy in CFT systems.

Formulas for open and finite temperature systems are derived.

Numerical validation in XY spin chain, Ising, and XX models.

Abstract

We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement entanglement entropy and the Casimir energy of floating objects. Then we provide formulas for the post measurement entanglement entropy for open and finite temperature systems. We also comment on the Affleck-Ludwig boundary entropy in the context of the post measurement entanglement entropy. Finally, we also provide some formulas regarding modular hamiltonians and entanglement spectrum in the after measurement systems. After through discussion regarding CFT systems we also provide some predictions regarding massive field theories. We then discuss a generic method to calculate the post measurement entanglement entropy in the free fermion systems. Using the method we study the post measurement entanglement entropy in the XY spin chain. We check numerically the CFT and the massive field theory results in the transverse field Ising chain and the XX model. In particular, we study the post meaurement entanglement entropy in the infinite, periodic and open critical transverse field Ising chain and the critical XX model. The effect of the temperature and the gap is also discussed in these models.