Entanglement and Pseudo Entanglement Dynamics versus Fusion in CFT

TL;DR

This paper explores the dynamics of entanglement and pseudo entropy in rational conformal field theory, linking fusion rules and operator product expansion coefficients through analytical formulas and examining their evolution over time.

Contribution

It introduces a novel formula connecting fusion coefficients, quantum dimensions, and OPE coefficients, and analyzes entanglement and pseudo entropy evolution in superpositions of operators in RCFT.

Findings

EE shows step-like evolution consistent with quasiparticle propagation

PE retains information for all operators, showing amplification effects

Reduced density matrix becomes block-diagonal as quasiparticles enter the subsystem

Abstract

The fusion rules and operator product expansion (OPE) serve as crucial tools in the study of operator algebras within conformal field theory (CFT). Building upon the vision of using entanglement to explore the connections between fusion coefficients and OPE coefficients, we employ the replica method and Schmidt decomposition method to investigate the time evolution of entanglement entropy (EE) and pseudo entropy (PE) for linear combinations of operators in rational conformal field theory (RCFT). We obtain a formula that links fusion coefficients, quantum dimensions, and OPE coefficients. We also identify two definition schemes for linear combination operators. Under one scheme, the EE captures information solely for the heaviest operators, while the PE retains information for all operators, reflecting the phenomenon of pseudo entropy amplification. Irrespective of the scheme employed, the EE demonstrates a step-like evolution, illustrating the effectiveness of the quasiparticle propagation picture for the general superposition of locally excited states in RCFT. From the perspective of quasiparticle propagation, we observe spontaneous block-diagonalization of the reduced density matrix of a subsystem when quasiparticles enter the subsystem.