Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains

TL;DR

This paper develops a unified conformal field theory approach to compute Renyi entanglement entropies for primary and descendant states in critical one-dimensional systems with boundaries, validated by numerical spin chain results.

Contribution

It provides universal formulas for the first two descendants in the identity family and demonstrates entanglement entropies' effectiveness in resolving degeneracies.

Findings

Universal expressions for descendant states' entanglement entropies.

Excellent agreement between theory and numerical spin chain data.

Entanglement entropies resolve degeneracies in critical lattice models.

Abstract

We discuss the Renyi entanglement entropies of descendant states in critical one-dimensional systems with boundaries, that map to boundary conformal field theories in the scaling limit. We unify the previous conformal-field-theory approaches to describe primary and descendant states in systems with both open and closed boundaries. We provide universal expressions for the first two descendants in the identity family. We apply our technique to critical systems belonging to different universality classes with non-trivial boundary conditions that preserve conformal invariance, and find excellent agreement with numerical results obtained for finite spin chains. We also demonstrate that entanglement entropies are a powerful tool to resolve degeneracy of higher excited states in critical lattice models.