Capacity of Entanglement in Local Operators

TL;DR

This paper investigates how the capacity of entanglement evolves over time in free fermionic and Yang-Mills theories, revealing it as a sensitive measure of entanglement structure with universal early-time peaks and connections to black hole information models.

Contribution

It introduces the capacity of entanglement as a new operator-sensitive measure and defines the normalized Page time to characterize its peak behavior in quantum field theories.

Findings

Capacity exhibits non-trivial time evolution with a universal early-time peak.

Normalized Page time characterizes the operator-dependent timescale of capacity's peak.

Evolution of capacity resembles that in black hole microcanonical and canonical ensembles.

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 Yang-Mills theory in four spacetime dimensions. Capacity has non-trivial 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 Renyi 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.