Entanglement in Fock space of random QFT states

Abstract

Entanglement in random states has turned into a useful approach to quantum thermalization and black hole physics. In this article, we refine and extend the 'random unitaries framework' to quantum field theories (QFT), and to include conserved charges. We show that in QFT, the connection between typical states, reduced subsystems and thermal dynamics is more transparent within the Fock basis. We provide generic formulae for the typical reduced density matrices and entanglement entropies of any given subset of particles. To illustrate our methods, we apply the generic framework to the simplest but non trivial cases, a massless scalar field in two dimensions and its generalization to the case of N scalar fields, including the large N limit. We find the effective temperature, by matching the reduced dynamics to a Gibbs ensemble, and derive the equation of state of the QFT. The deviations from perfect thermality are shown to be of order 1/S instead of exp( S), a result which might be relevant for black hole physics. Finally we describe the analogue of the so-called 'Page curve' in the QFT scenario as a function of the energy scale which divides high from low energy degrees of freedom.