Proof of the universal density of charged states in QFT

Abstract

We prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT at high energies for global symmetries associated with finite groups. An equivalent statement, based on the entropic order parameter associated with charged operators in the thermofield double state, was proven in a previous article by Casini, Huerta, Pontello, and the present author. Here we describe how the statement about the entropic order parameter arises, and how it gets transformed into the universal density of states. The use of the certainty principle, relating the entropic order and disorder parameters, is crucial for the proof. We remark that although the immediate application of this result concerns charged states, the origin and physics of such density can be understood by looking at the vacuum sector only. We also describe how these arguments lie at the origin of the so-called entropy equipartition in these type of systems, and how they generalize to QFT’s on non-compact manifolds.

Snowmass white paper: Quantum information in quantum field theory and quantum gravity

“…This universal form is in turn related to the form of the high temperature density of states of the theory defined on a compact space. This form was conjecture in [249] and proven in [250]. It is also related to the equipartition property [251] for symmetry resolved entanglement.…”

Lectures on entanglement in quantum field theory

“…The asymptotic density of charged states was conjectured by D. Harlow and H. Ooguri in [100]. The proof using the certainty relation is by J. M. Magan in [101]. This last paper also contains a discussion of the relation of this topic with the so-called "entanglement equipartition" in the symmetry-resolved entanglement entropy [102,103].…”

Lectures on entanglement in quantum field theory

“…The asymptotic density of charged states was conjectured by D. Harlow and H. Ooguri in [100]. The proof using the certainty relation is by J. M. Magan in [101]. This last paper also contains a discussion of the relation of this topic with the so-called "entanglement equipartition" in the symmetry-resolved entanglement entropy [102,103].…”