Entanglement constant for conformal families

TL;DR

This paper demonstrates that in 1+1D conformal field theories, local operator excitations increase Renyi entropies by a universal constant, which is linked to the quantum dimension in rational theories, serving as an intrinsic operator characteristic.

Contribution

It introduces the concept of an entanglement constant for conformal families, linking local operator excitations to a universal entanglement measure across the family.

Findings

The entanglement increase is constant for all members of a conformal family.

In rational CFTs, the constant equals the logarithm of the quantum dimension.

Provides detailed examples and a general derivation for the second Renyi entropy.

Abstract

We show that in 1+1 dimensional conformal field theories, exciting a state with a local operator increases the Renyi entanglement entropies by a constant which is the same for every member of the conformal family. Hence, it is an intrinsic parameter that characterises local operators from the perspective of quantum entanglement. In rational conformal field theories this constant corresponds to the logarithm of the quantum dimension of the primary operator. We provide several detailed examples for the second Renyi entropies and a general derivation.