  In a quantum many-body system that possesses an additive conserved quantity,
the entanglement entropy of a subsystem can be resolved into a sum of
contributions from different sectors of the subsystem's reduced density matrix,
each sector corresponding to a possible value of the conserved quantity. Recent
studies have discussed the basic properties of these symmetry-resolved
contributions, and calculated them using conformal field theory and numerical
methods. In this work we employ the generalized Fisher-Hartwig conjecture to
obtain exact results for the characteristic function of the symmetry-resolved
entanglement ("flux-resolved entanglement") for certain 1D spin chains, or,
equivalently, the 1D fermionic tight binding and the Kitaev chain models. These
results are true up to corrections of order $o(L^{-1})$ where $L$ is the
subsystem size. We confirm that this calculation is in good agreement with
numerical results. For the gapless tight binding chain we report an intriguing
periodic structure of the characteristic functions, which nicely extends the
structure predicted by conformal field theory. For the Kitaev chain in the
topological phase we demonstrate the degeneracy between the even and odd
fermion parity sectors of the entanglement spectrum due to virtual Majoranas at
the entanglement cut. We also employ the Widom conjecture to obtain the leading
behavior of the symmetry-resolved entanglement entropy in higher dimensions for
an ungapped free Fermi gas in its ground state.
