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

Abstract

In this paper, we use the replica approach to study the Rényi 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 Rényi 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.

JHEP version, add more physical discussions on the results

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Cited by in corpus (16)

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• Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity
• Correlation functions of the CFTs on torus with $T\bar{T}$ deformation
• Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
• Double Local Quenches in 2D CFTs and Gravitational Force
• Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs
• Entanglement and chaos in warped conformal field theories
• On the real-time evolution of pseudo-entropy in 2d CFTs
• New Properties of Large-$c$ Conformal Blocks from Recursion Relation
• Entanglement Entropy after Double-Excitation as Interaction Measure
• Entanglement spreading after local fermionic excitations in the XXZ chain
• Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians
• From locality to irregularity: Introducing local quenches in massive scalar field theory
• Sum rule for the pseudo-Rényi entropy
• Entanglement spreading after local and extended excitations in a free-fermion chain