Symmetry-Resolved Entanglement of $C_2$-symmetric Topological Insulators

For a many-body system of arbitrary dimension, we consider fermionic ground states of non-interacting Hamiltonians invariant under a $C_2$ cyclic group. The absolute difference $\mathrm{\Delta }$ between the number of occupied symmetric and anti-symmetric single-particle states is an adiabatic invariant. We prove lower bounds on the configurational and the number entropy based on this invariant. In band insulators, the topological invariant $\mathrm{\Delta }$ and the entropy bounds can be directly determined from high symmetry points in the Brillouin zone.