Physics at the entangling surface

TL;DR

This paper explores the role of the entangling surface in quantum field theories, showing how boundary choices affect entanglement and demonstrating a connection between entanglement entropy and Cardy states in 2D CFTs.

Contribution

It clarifies the boundary conditions at the entangling surface and links entanglement entropy in the Ising chain to conformal boundary states.

Findings

Small physical boundary at the entangling surface is implicitly introduced.

Entanglement entropy in the critical Ising chain encodes Cardy states.

Boundary conditions influence the structure of the Hilbert space in QFT.

Abstract

To consider the entanglement between the spatial region $A$ and its complement in a QFT, we need to assign a Hilbert space $\mathcal{H}_A$ to the region, by making a certain choice on the boundary $\partial A$. We argue that a small physical boundary is implicitly inserted at the entangling surface. We investigate these issues in the context of 2d CFTs, and show that we can indeed read off the Cardy states of the $c=1/2$ minimal model from the entanglement entropy of the critical Ising chain.