Maximally entangled mode, metal-insulator transition, and violation of entanglement area law in noninteracting fermion ground states

Abstract

We study in this work the ground-state entanglement properties of two models of noninteracting fermions moving in one dimension, that exhibit metal-insulator transitions. We find that entanglement entropy grows either logarithmically or in a power-law fashion in the metallic phase, thus violating the (one-dimensional version of) entanglement area law. No such violation is found in the insulating phase. We further find that characteristics of single fermion states at the Fermi energy (which can not be obtained from the many-fermion Slater determinant) is captured by the lowest energy single fermion mode of the entanglement Hamiltonian; this is particularly true at the metal-insulator transition point. Our results suggest entanglement is a powerful way to detect metal-insulator transitions, without knowledge of the Hamiltonian of the system.