Symmetry-resolved entanglement of C2 -symmetric topological insulators

Abstract

For a many-body system of arbitrary dimension, we consider fermionic ground states of noninteracting Hamiltonians invariant under a ${C}_{2}$ cyclic group. The absolute difference $\mathrm{\ensuremath{\Delta}}$ between the number of occupied symmetric and antisymmetric single-particle states is a topological invariant in this case. We prove lower bounds on the configurational and the number entropy based on this invariant. Entanglement entropies are particularly important for identifying topological phases protected by spatial symmetries because they lack gapless boundary modes in general. In topological crystalline insulators, the topological invariant $\mathrm{\ensuremath{\Delta}}$ and the entropy bounds can be directly determined from high-symmetry points in the Brillouin zone.