Particle Number Fluctuations, Renyi Entropy, And Symmetry-Resolved Entanglement Entropy In A Two-Dimensional Fermi Gas From Multidimensional Bosonization

We revisit the computation of particle number fluctuations and the Renyi entanglement entropy of a two-dimensional Fermi gas using multidimensional 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 Renyi 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 ln R, the symmetry-resolved entanglement scales as root R ln R, where R is the radius of the subregion of our interest.