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 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.
Highlights
Well suited for characterizing topologically ordered states [28]
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
We have studied the time evolution of excess value of the capacity of entanglement in free, massless fermionic theory and free Yang-Mills theory in four spacetime dimensions
Summary
We first briefly introduce the capacity of entanglement and consider an example [20] where it can be compared with other quantities like entanglement and Rényi entropies. Note that for the cases we consider here, the regulator will not appear in the expression of entropies and capacity as we take the → 0 limit This contrasts with the 2d holographic CFTs, where the entropies are not saturated at late times, but they diverge as log(t/ ). One crucial difference between capacity and Rényi/entanglement entropies is that capacity always shows a peak at early times for any γ. Note that for γ = ±1, Rényi entropies take different values for different m at late times while the capacity takes a universal peak value and depends only on the inserted operator. The peak happens at a partially entangled state, and the operators can be characterized by the time where capacity shows the maximum universal value. This implies capacity could, in principle, give enough information of the inserted operator, especially at early times
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
