Entanglement entropies of minimal models from null-vectors

TL;DR

This paper introduces a novel method leveraging null-vector conditions to compute Rénnyi entropies in 1D critical systems, demonstrated on the non-unitary Yang-Lee model, combining differential equations and bootstrap techniques.

Contribution

It develops a new approach using null-vector conditions and bootstrap methods to calculate entanglement entropies in critical models.

Findings

Derived differential equations for twist field correlators.

Successfully applied method to the Yang-Lee model.

Provided explicit Rénnyi entropy calculations for non-unitary systems.

Abstract

We present a new method to compute R\'enyi entropies in one-dimensional critical systems. The null-vector conditions on the twist fields in the cyclic orbifold allow us to derive a differential equation for their correlation functions. The latter are then determined by standard bootstrap techniques. We apply this method to the calculation of various R\'enyi entropies in the non-unitary Yang-Lee model.