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.
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Acknowledgments
We would like to thank Tadashi Takayanagi, Wu-zhong Guo, Yuya Kusuki, Yuan Sun, Hao Ouyang, Hong-An Zeng, and Yang Liu for their valuable discussions related to this work. We are also grateful to all the organizers of the “Quantum Information, Quantum Matter and Quantum Gravity” workshop (YITP-T-23-01) held at YITP, Kyoto University, where a part of this work was done. SH would like to appreciate the financial support from Jilin University, Max Planck Partner Group, and the Natural Science Foundation of China Grants (No.12075101, No.12235016). L.Z and Z.Z are supported by the Science and Technology Development Plan Project of Jilin Province, China (No. 20240101326JC).
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He, S., Zhang, YX., Zhao, L. et al. Entanglement and pseudo entanglement dynamics versus fusion in CFT. J. High Energ. Phys. 2024, 177 (2024). https://doi.org/10.1007/JHEP06(2024)177
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DOI: https://doi.org/10.1007/JHEP06(2024)177