Fermion Parity Resolution of Entanglement

Abstract: Entanglement is analyzed in the Majorana fermion conformal field theory (CFT) in the vacuum, in the fermion state, and in states built from conformal interfaces. In the boundary-state approach, Hilbert space admits two factorizations for a single interval, producing distinct entanglement spectra determined by spin structures. Although R\'enyi and relative entropiesare shown to be insensitive to these structures, symmetry-resolved entanglement naturally reveals their differences. The Majorana fermion's $\mathbb{Z}_2^F$ symmetry, generated by the fermion-parity operator $F$, distinguishes bosonic from fermionic sectors, motivating the notion of fermion-parity resolution. While $\mathbb{Z}_2^F$ is naturally a symmetry of the vacuum and fermion reduced density matrices, the Hilbert space factorization is shown to stabilize this symmetry in conformal interface states. When a Majorana zero mode is present, fermion-parity-resolved entropies display equipartition at all orders in the UV cutoff; in its absence, the breaking of equipartition is quantified by Ramond-sector data. This behavior persists across all states considered. Connections with symmetry-protected topological phases of matter are outlined. All results are compared with twist field computations.