# Symmetry resolved entanglement in free fermionic systems

## TL;DR

This paper analyzes the asymptotic behavior of symmetry-resolved entanglement entropies in one-dimensional free fermionic systems, providing exact constants and corrections, and extends the results to free Fermi gases.

## Contribution

It applies the Fisher-Hartwig conjecture to derive detailed asymptotics of symmetry-resolved entanglement, including non-universal constants and oscillatory terms, in free fermionic models.

## Key findings

- Exact asymptotic formulas for symmetry-resolved entanglement entropies.
- Identification of oscillatory subleading contributions.
- Extension of results to one-dimensional free Fermi gases.

## Abstract

We consider the symmetry resolved R\'enyi entropies in the one dimensional tight binding model, equivalent to the spin-1/2 XX chain in a magnetic field. We exploit the generalised Fisher-Hartwig conjecture to obtain the asymptotic behaviour of the entanglement entropies with a flux charge insertion at leading and subleading orders. The o(1) contributions are found to exhibit a rich structure of oscillatory behaviour. We then use these results to extract the symmetry resolved entanglement, determining exactly all the non-universal constants and logarithmic corrections to the scaling that are not accessible to the field theory approach. We also discuss how our results are generalised to a one-dimensional free fermi gas.