Symmetry Protected Bulk-Boundary Correspondence in Interacting Topological Insulators
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| Format: | Preprint |
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2026
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| _version_ | 1866918445285638144 |
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| author | Estake, Kiran Babasaheb Roy, Dibyendu |
| author_facet | Estake, Kiran Babasaheb Roy, Dibyendu |
| contents | 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 $4^ν$ scaling with the winding number $ν$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_09801 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetry Protected Bulk-Boundary Correspondence in Interacting Topological Insulators Estake, Kiran Babasaheb Roy, Dibyendu Mesoscale and Nanoscale Physics 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 $4^ν$ scaling with the winding number $ν$, 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. |
| title | Symmetry Protected Bulk-Boundary Correspondence in Interacting Topological Insulators |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2604.09801 |