Particle Number Fluctuations, R\'{e}nyi and Symmetry-resolved Entanglement Entropy in Two-dimensional Fermi Gas from Multi-dimensional Bosonization

TL;DR

This paper uses multi-dimensional bosonization to analyze particle fluctuations and entanglement entropy in a 2D Fermi gas, revealing logarithmic violations of the area law and symmetry-resolved entanglement scaling.

Contribution

It provides a detailed calculation of entanglement properties in 2D Fermi gases with circular Fermi surfaces using multi-dimensional bosonization, confirming the Widom conjecture.

Findings

Both particle fluctuations and Rènyi entropy show logarithmic area law violation.

Total entanglement entropy scales as R log R.

Symmetry-resolved entanglement scales as sqrt(R log R).

Abstract

In this paper, we revisit the computation of particle number fluctuations and the R\'{e}nyi entanglement entropy of a two-dimensional Fermi gas using multi-dimensional bosonization. In particular, we compute these quantities for a circular Fermi surface and a circular entangling surface. Both quantities display a logarithmic violation of the area law, and the R\'{e}nyi entropy agrees with the Widom conjecture. Lastly, we compute the symmetry-resolved entanglement entropy for the two-dimensional circular Fermi surface and find that, while the total entanglement entropy scales as $R\log R$, the symmetry-resolved entanglement scales as $\sqrt{R\log R}$, where $R$ is the radius of the subregion of our interest.