Entanglement in spatially inhomogeneous many-fermion systems

TL;DR

This paper introduces a local-density approximation method to quantify entanglement entropy in spatially inhomogeneous many-fermion systems, revealing significant differences from homogeneous systems.

Contribution

It proposes a novel LDA-based approach to evaluate entanglement entropy in inhomogeneous environments, applicable to various physical models.

Findings

Entanglement entropy differs markedly between inhomogeneous and homogeneous systems.

The LDA scheme effectively captures entanglement in complex inhomogeneous setups.

Applications include models of electrons in superlattices, impurity-laden wires, and confined quantum systems.

Abstract

We investigate entanglement of strongly interacting fermions in spatially inhomogeneous environments. To quantify entanglement in the presence of spatial inhomogeneity, we propose a local-density approximation (LDA) to the entanglement entropy, and a nested LDA scheme to evaluate the entanglement entropy on inhomogeneous density profiles. These ideas are applied to models of electrons in superlattice structures with different modulation patterns, electrons in a metallic wire in the presence of impurities, and phase-separated states in harmonically confined many-fermion systems, such as electrons in quantum dots and atoms in optical traps. We find that the entanglement entropy of inhomogeneous systems is strikingly different from that of homogeneous systems.