Entanglement and particle fluctuations of one-dimensional chiral topological insulators

We consider the topological protection of entanglement and particle fluctuations for a general one-dimensional chiral topological insulator with winding number I. We prove, in particular, that when the periodic system is divided spatially into two equal halves, the single-particle entanglement spectrum has 2|I| protected eigenvalues at 1/2. Therefore the number fluctuations are bounded from below by ΔN2≥|I|/2 and the entanglement entropy by S≥2|I|ln2. We note that our results are obtained by applying directly an index theorem to the microscopic model and do not rely on an equivalence to a continuum model or a bulk-boundary correspondence for a slowly varying boundary. © 2023 American Physical Society.