Role of spatial higher order derivatives in momentum space entanglement

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.