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Particle Number Fluctuations, Rényi and Symmetry-resolved Entanglement Entropy in Two-dimensional Fermi Gas from Multi-dimensional Bosonization

In this paper, we revisit the computation of particle number fluctuations and the Rényi 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 Rényi 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.