Entanglement Entropy and Twist Fields

TL;DR

This paper explores the calculation of entanglement entropy in 2D critical systems using replica and conformal field theory methods, highlighting agreements and discrepancies in multi-interval cases.

Contribution

It compares numerical replica approach results with conformal field theory predictions, explaining discrepancies for multi-interval subsystems.

Findings

Perfect agreement for single-interval subsystems.

Discrepancies arise for multi-interval subsystems.

Analysis clarifies reasons for differences in methods.

Abstract

The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as the vacuum expectation value of a suitable observable in a system made with n independent copies of the original system. We use this property to numerically evaluate it in some two-dimensional critical systems, where it can be compared with the results of Calabrese and Cardy, who wrote the same quantity in terms of correlation functions of twist fields of a conformal field theory. Although the two calculations match perfectly even in finite systems when the analyzed subsystem consists of a single interval, they disagree whenever the subsystem is composed of more than one connected part. The reasons of this disagreement are explained.