Entanglement scaling in critical two-dimensional fermionic and bosonic systems

TL;DR

This paper investigates how entanglement scales in critical two-dimensional fermionic and bosonic systems, revealing different behaviors depending on the nature of the Fermi surface and confirming theoretical predictions.

Contribution

It provides an exact calculation of bipartite entanglement scaling in 2D critical systems, unifying fermionic and bosonic models through Green's functions.

Findings

Fermionic systems show a logarithmic correction to the area law with chemical potential dependence.

Zero-dimensional Fermi surfaces lead to an area law with sublogarithmic correction.

Bosonic systems follow the area law without additional corrections.

Abstract

We relate the reduced density matrices of quadratic bosonic and fermionic models to their Green's function matrices in a unified way and calculate the scaling of bipartite entanglement of finite systems in an infinite universe exactly. For critical fermionic 2D systems at T=0, two regimes of scaling are identified: generically, we find a logarithmic correction to the area law with a prefactor dependence on the chemical potential that confirms earlier predictions based on the Widom conjecture. If, however, the Fermi surface of the critical system is zero-dimensional, we find an area law with a sublogarithmic correction. For a critical bosonic 2D array of coupled oscillators at T=0, our results show that entanglement follows the area law without corrections.