Symmetry and the resulting conservation laws have long been known to play a unique role in quantum many body states in condensed matter and high energy physics; more recently, the central importance of entanglement entropy has also been recognized. In our work [1] we study the interplay of these two fundamental concepts:  Given a conserved quantity in the system, the entanglement entropy of a subsystem can be resolved into a sum of contributions, each of which arising from states where the subsystem possesses a specific possible value of this quantity out of the total conserved value. Studying these symmetry-resolved contributions provides insight into the internal structure of the entanglement, beyond what can be learned from the value of the entanglement entropy itself. We present exact analytical results for the symmetry-resolved entanglement entropy in the Kitaev chain model, and demonstrate that in the topological phase there is a degeneracy between the even and odd fermion parity sectors of the entanglement spectrum, due to virtual Majoranas at the entanglement cut. These virtual Majoranas mirror the Majorana zero-modes hosted by the physical edges of the open Kitaev chain. Therefore, this result rigorously attests to the strong connection between entanglement and topological quantum phase transitions. We also obtain the leading behavior of the symmetry-resolved entanglement entropy for an ungapped free Fermi gas in a general dimension, and present exact results for the special case of the gapless 1D fermionic tight binding chain, which have a natural interpretation from a conformal field theory perspective.

[1] S. Fraenkel and M. Goldstein, Symmetry resolved entanglement: Exact results in 1D and beyond, arXiv:1910.08459.