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arXiv:1702.08655 · Physical review. D/Physical review. D.

Role of spatial higher order derivatives in momentum space entanglement

Srijan Kumar, S. Shankaranarayanan

Published Mar 24, 2017• 12 citations
arXivHTMLPDF

Abstract

We study the momentum space entanglement between different energy modes of interacting scalar fields propagating in general ($D+1$)-dimensional flat space-time. As opposed to some of the recent works [V. Balasubramanian et al., Phys. Rev. D 86, 045014 (2012)], we use a Lorentz invariant normalized ground state to obtain the momentum space entanglement entropy. We show that the Lorenz invariant definition removes the spurious power-law behavior obtained in the earlier works. More specifically, we show that the cubic interacting scalar field in ($1+1$) dimensions leads to logarithmic divergence of the entanglement entropy and is consistent with the results from real space entanglement calculations. We study the effects of the introduction of the Lorentz violating higher derivative terms in the presence of a nonlinear self-interacting scalar field potential and show that the divergence structure of the entanglement entropy is improved in the presence of spatial higher derivative terms.

DOI
10.1103/physrevd.95.065023

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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 a connection further by developing a novel method to calculate the R\'enyi 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.
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