Symmetry-resolved entanglement of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>C</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> -symmetric topological insulators

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