Probing Hawking radiation through capacity of entanglement

Abstract

We consider the capacity of entanglement in models related with the gravitational phase transitions. The capacity is labeled by the replica parameter which plays a similar role to the inverse temperature in thermodynamics. In the end of the world brane model of a radiating black hole the capacity has a peak around the Page time indicating the phase transition between replica wormhole geometries of different types of topology. Similarly, in a moving mirror model describing Hawking radiation the capacity typically shows a discontinuity when the dominant saddle switches between two phases, which can be seen as a formation of island regions. In either case we find the capacity can be an invaluable diagnostic for a black hole evaporation process.

Capacity of entanglement in local operators

“…In general, the capacity shows very different behavior than entanglement or Rényi entropies, although the capacity and entanglement entropy might be equal in some cases [20]. An interesting behavior of capacity was observed in the context of information paradox [24]. In the end of the world (EoW) brane model [49] the capacity exhibits a peak at Page time and indicates a phase transition between a fully disconnected and a fully connected geometry of replica wormholes.…”

“…Interestingly, the peak value of capacity turns out to be universal. We call it "Page time" 2 due to the close resemblance with the evolution of capacity in replica geometry [24]. However, we do not have any black holes in our case.…”

“…On a somewhat different note, an information-theoretic quantity, known as the capacity of entanglement [20][21][22][23] or capacity in short, recently gained some attention, for example, in the context of the information paradox [24,25]. It was shown that, like entanglement entropy, capacity could also truly probe the phase transition that happens at the Page time [24,25]. It either shows a peak or changes discontinuously between two phases at Page time, similar in spirit to the subregion complexity [26,27].…”

“…Although less familiar, capacity has been studied in condensed matter systems like the Kitaev model, and it appears to be JHEP07(2021)019 well suited for characterizing topologically ordered states [28]. It is defined via the second derivative of Rényi entropy S (m) A with respect to the replica parameter [20,24]…”

Spectrum of end of the world branes in holographic BCFTs

“…We also refer to [28,29] for studies utilizing such branes to compute the entropy of Hawking radiation of higher dimensional black holes. End of the world branes also play a crucial role to find holographic duals of moving mirrors [30,31], which mimic black hole evaporation processes.…”