Entanglement Entropy from TFD Entropy Operator

TL;DR

This paper introduces a canonical method for directly computing entanglement entropy in two-dimensional conformal theories on a torus using the TFD entropy operator, avoiding analytic continuation from Rènyi entropy.

Contribution

It presents a novel approach to calculate entanglement entropy directly from the entropy operator in conformal theories, simplifying the process and providing a model for its linear growth over time.

Findings

Entanglement entropy can be computed directly from the TFD entropy operator.

The method applies to 2D conformal theories on a torus with specific moduli.

Entanglement entropy exhibits linear growth with time.

Abstract

In this work, a canonical method to compute entanglement entropy is proposed. We show that for two-dimensional conformal theories defined in a torus, a choice of moduli space allows the typical entropy operator of the TFD to provide the entanglement entropy of the degrees of freedom defined in a segment and their complement. In this procedure, it is not necessary to make an analytic continuation from the R\'enyi entropy and the von Neumann entanglement entropy is calculated directly from the expected value of an entanglement entropy operator. We also propose a model for the evolution of the entanglement entropy and show that it grows linearly with time.