# Role of spatial higher order derivatives in momentum space entanglement

## TL;DR

This paper investigates how higher order spatial derivatives influence momentum space entanglement entropy in scalar fields, revealing that Lorentz invariant definitions remove unphysical divergences and that higher derivatives can improve divergence behavior.

## Contribution

It introduces a Lorentz invariant approach to compute momentum space entanglement entropy and demonstrates how higher derivative terms affect divergence structures in scalar field theories.

## Key findings

- Lorentz invariant ground state removes spurious power-law divergences.
- Logarithmic divergence observed in (1+1)D cubic scalar field.
- Higher derivative terms improve divergence behavior of entanglement entropy.

## 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 [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.