Entanglement entropy and quantum field theory: a non-technical introduction

TL;DR

This work develops a non-technical QFT framework for entanglement entropy, focusing on 1+1D systems at quantum criticality described by a 2D CFT. Using path-integral methods and conformal transformations, it derives universal scaling forms for the entanglement entropy across various geometries (single interval, finite temperature, finite size, boundaries, and multi-intervals) and expresses them in terms of the central charge. It further analyzes non-critical (massive) 1+1D models, showing how the entropy crosses over to a log scaling with the correlation length and validating the predictions via Ising and related models. The results illuminate how geometry, temperature, and boundary conditions shape quantum entanglement in critical and near-critical 1D systems, providing exact, universal benchmarks for many-body quantum information in field theories.

Abstract

In these proceedings we give a pedagogical and non-technical introduction to the Quantum Field Theory approach to entanglement entropy. Particular attention is devoted to the one space dimensional case, with a linear dispersion relation, that, at a quantum critical point, can be effectively described by a two-dimensional Conformal Field Theory.

Figures (2)

• Figure 1: Path integral representation of $\rho_A$.
• Figure 2: Entanglement entropy for the 1D Ising chain as function of $\lambda$.