Capacity of entanglement in local operators
Abstract
We study the time evolution of the excess value of capacity of entanglement between a locally excited state and ground state in free, massless fermionic theory and free YangMills theory in four spacetime dimensions. Capacity has nontrivial time evolution and is sensitive to the partial entanglement structure, and shows a universal peak at early times. We define a quantity, the normalized "Page time", which measures the timescale when capacity reaches its peak. This quantity turns out to be a characteristic property of the inserted operator. This firmly establishes capacity as a valuable measure of entanglement structure of an operator, especially at early times similar in spirit to the Rényi entropies at late times. Interestingly, the time evolution of capacity closely resembles its evolution in microcanonical and canonical ensemble of the replica wormhole model in the context of the black hole information paradox.
 Publication:

Journal of High Energy Physics
 Pub Date:
 July 2021
 DOI:
 10.1007/JHEP07(2021)019
 arXiv:
 arXiv:2106.00228
 Bibcode:
 2021JHEP...07..019N
 Keywords:

 Conformal Field Theory;
 Field Theories in Higher Dimensions;
 Field Theories in Lower Dimensions;
 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics;
 Quantum Physics
 EPrint:
 26 Pages, 9 figures, Minor changes, references added, accepted for publication in JHEP