Symmetry Protected Bulk-Boundary Correspondence in Interacting Topological Insulators

TL;DR

This paper establishes a quantitative bulk-boundary correspondence in interacting topological insulators by linking many-body invariants to entanglement spectrum degeneracies, extending topological classification beyond single-particle models.

Contribution

It introduces a gauge-invariant many-body winding invariant based on geometric phases that predicts entanglement degeneracies and demonstrates robustness under interactions and disorder.

Findings

The invariant exhibits a universal $4^ u$ scaling with the winding number.

The correspondence is robust under interactions and symmetry-preserving disorder.

Inversion symmetry stabilizes the quantization of the invariant and degeneracies.

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.