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Theoretische Physik III

Würzburg Seminar on Quantum Field Theory and Gravity

Renormalization group as a quantum channel, momentum space entanglement, and the separability of fixed points
Datum: 06.12.2022, 14:15 - 15:15 Uhr
Veranstalter: Lehrstuhl für Theoretische Physik III
Vortragende*r: Flavio Nogueira

The entanglement between momentum modes of a quantum field theory at different scales is not as well studied as its counterpart in real space, despite the natural connection with the Wilsonian idea of integrating out the high-momentum degrees of freedom. In this talk we will elaborate on a novel method to calculate the Rényi and entanglement entropies between slow and fast modes, which is based on the Wilsonian effective action at a given scale.  This method is easily generalized to higher-order or nonperturbative calculations and has the advantage of avoiding matrix diagonalizations of other techniques. Further, we show that the Wilson renormalization group defines a quantum channel acting on the momentum-space density matrices of a quantum field theory. This interpretation of the RG allows us to derive a remarkable property for the vacuum of theories at a fixed point: they have no entanglement between momentum scales. Our result can be interpreted as a consequence of the scale symmetry of such theories and leads to constraints on the form of the ground state and on expectation values of momentum space operators.

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