  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 [1], we use Lorentz
invariant normalized ground state to obtain the momentum space entanglement
entropy. We show that the Lorenz invariant definition removes the spurious
power-law behaviour obtained in the earlier works [1]. More specifically, we
show that the cubic interacting scalar field in (1 + 1) dimensions leads to
logarithmic divergence of the entanglement entropy and 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 non-linear self inter- acting scalar field potential and show that the
divergence structure of the entanglement entropy is improved in the presence of
spatial higher derivative terms.
