Entanglement entropy in (1+1)D CFTs with multiple local excitations

TL;DR

This paper investigates the entanglement entropy of multiple local excitations in (1+1)D conformal field theories using replica and algebraic methods, revealing deep structural identities.

Contribution

It establishes the equivalence of two entropy calculations and derives algebraic identities in rational CFTs, linking quantum information and CFT structure.

Findings

Proves $S_L = S_R$ for local excitations in (1+1)D CFTs.

Derives algebraic identities involving $F$ symbols and quantum dimensions.

Provides a complete framework connecting entanglement measures and CFT algebraic structure.

Abstract

In this paper, we use the replica approach to study the R\'enyi entropy $S_L$ of generic locally excited states in (1+1)D CFTs, which are constructed from the insertion of multiple product of local primary operators on vacuum. Alternatively, one can calculate the R\'enyi entropy $S_R$ corresponding to the same states using Schmidt decomposition and operator product expansion, which reduces the multiple product of local primary operators to linear combination of operators. The equivalence $S_L=S_R$ translates into an identity in terms of the $F$ symbols and quantum dimensions for rational CFT, and the latter can be proved algebraically. This, along with a series of papers, gives a complete picture of how the quantum information quantities and the intrinsic structure of (1+1)D CFTs are consistently related.