Entanglement and particle fluctuations of one-dimensional chiral topological insulators

Abstract

We consider the topological protection of entanglement and particle fluctuations for a general one-dimensional chiral topological insulator with winding number $\mathcal{I}$. We prove, in particular, that when the periodic system is divided spatially into two equal halves, the single-particle entanglement spectrum has $2|\mathcal{I}|$ protected eigenvalues at $1/2$. Therefore the number fluctuations are bounded from below by $\Delta N^2\ge |\mathcal{I}|/2$ and the entanglement entropy by $S\ge 2|\mathcal{I}|\ln 2$. 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 slow varying boundary.

6 pages, published version

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Cited by in corpus (5)

• Hidden zero modes and topology of multiband non-Hermitian systems
• Symmetry-Resolved Entanglement: General considerations, calculation from correlation functions, and bounds for symmetry-protected topological phases
• Formal Green's function theory in non-Hermitian lattice systems
• Topological Properties of Single-Particle States Decaying into a Continuum due to Interaction
• Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values