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arXiv · 2604.09801

Symmetry Protected Bulk-Boundary Correspondence in Interacting Topological Insulators

Kiran Babasaheb Estake·Dibyendu Roy
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Abstract

We establish a quantitative bulk-boundary correspondence in interacting topological insulators by relating many-body topological invariants to characteristic degeneracy structures in the entanglement spectrum. Focusing on generalized Su-Schrieffer-Heeger chains with higher winding number, we construct a gauge-invariant many-body winding invariant based on Pancharatnam geometric phases that remains well defined in the presence of interactions. We show that this invariant uniquely determines the low-lying entanglement-spectrum degeneracy, which exhibits a universal $4^\nu$ scaling with the winding number $\nu$, providing a concrete formulation of bulk-boundary correspondence beyond single-particle topology. Using exact diagonalization, we demonstrate the robustness of this correspondence under interactions and symmetry-preserving disorder, and identify inversion symmetry as a minimal protecting symmetry that stabilizes both the quantization of the invariant and the associated entanglement degeneracies. Our results unify geometric-phase invariants and entanglement diagnostics within a many-body framework and provide a route to identifying interacting topological phases beyond band theory.

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Kiran Babasaheb Estake, Dibyendu Roy. 2026-04-10. Symmetry Protected Bulk-Boundary Correspondence in Interacting Topological Insulators. https://arxiv.org/abs/2604.09801

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