Entanglement negativity in two-dimensional free lattice models

TL;DR

This paper investigates how entanglement, measured by logarithmic negativity, scales in two-dimensional free lattice models, revealing an area law for harmonic oscillators and a logarithmic correction for fermionic models, with a conjectured formula relating to Fermi surface geometry.

Contribution

It introduces a conjecture for the entanglement negativity scaling in fermionic models based on Fermi surface geometry, supported by numerical evidence.

Findings

Harmonic oscillator models follow a strict area law.

Fermionic models exhibit a logarithmic correction to the area law.

The conjectured formula accurately predicts the correction based on geometry.

Abstract

We study the scaling properties of the ground-state entanglement between finite subsystems of infinite two-dimensional free lattice models, as measured by the logarithmic negativity. For adjacent regions with a common boundary, we observe that the negativity follows a strict area law for a lattice of harmonic oscillators, whereas for fermionic hopping models the numerical results indicate a multiplicative logarithmic correction. In this latter case, we conjecture a formula for the prefactor of the area-law violating term, which is entirely determined by the geometries of the Fermi surface and the boundary between the subsystems. The conjecture is tested against numerical results and a good agreement is found.