Entanglement signatures of phase transition in higher-derivative quantum field theories

We show that the variation of the ground state entanglement in linear, higher spatial derivatives field theories at zero-temperature have signatures of phase transition. Around the critical point, when the dispersion relation changes from linear to non-linear, there is a fundamental change in the reduced density matrix leading to a change in the scaling of entanglement entropy. We suggest possible explanations involving both kinematical and dynamical effects. We discuss the implication of our work for 2-D condensed matter systems, black-hole entropy and models of quantum gravity.