Momentum Space Entanglement from the Wilsonian Effective Action

Abstract

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. Here, we push such connection further by developing 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 procedure is applied to the perturbative regime of some scalar theories, comparing the lowest-order results with those from the literature and interpreting them in terms of Feynman diagrams. This method is easily generalized to higher-order or nonperturbative calculations. It has the advantage of avoiding matrix diagonalizations of other techniques.

v2: minor changes (added a little more discussion on the applicability of the method to gauge theories), references added, 17 pages, 15 Figures; nearly matches published version

References in corpus (4)

• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Entanglement entropy in lattice gauge theories
• Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators

Cited by in corpus (9)

• Temporal Entanglement Entropy as a probe of Renormalization Group Flow
• Perturbative unitarity bounds from momentum-space entanglement
• Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points
• Positivity in Amplitudes and Quantum Entanglement
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
• A Lindbladian for exact renormalization of density operators in QFT
• Superselection Rules, Bosonization Duality in 1+1 Dimensions and Momentum-Space Entanglement
• Holographic entanglement renormalisation for fermionic quantum matter
• Geometric Rényi mutual information induced by localized particle excitations in quantum field theory