A One-Particle Density Matrix Framework for Mode-Shell Correspondence: Characterizing Topology in Amorphous Higher-Order Topological Insulators
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arXiv
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| Format: | Preprint |
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2025
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| author | Martínez, Miguel F. Jezequel, Lucien Bardarson, Jens H. Kvorning, Thomas Klein Hannukainen, Julia D. |
| author_facet | Martínez, Miguel F. Jezequel, Lucien Bardarson, Jens H. Kvorning, Thomas Klein Hannukainen, Julia D. |
| contents | We present a framework for characterizing higher-order topological phases directly from the one-particle density matrix, without any reference to an underlying Hamiltonian. Our approach extends the mode-shell correspondence, originally formulated for single-particle Hamiltonians, to Gaussian states subject to chiral constraints. In this correspondence, the mode index counts topological boundary modes, while the shell index quantifies the bulk topology in a region surrounding the modes, providing a bulk-boundary diagnostic. In one-dimensional topological insulators, the shell index reduces to the local chiral marker, recovering the winding number in the translation-invariant limit. We apply the mode-shell correspondence to a $C_4$-symmetric higher-order topological insulator with a chiral constraint and show that a fractional shell index implies that the higher-order phase is intrinsic. The one-particle density matrix is formulated in real space, so the mode-shell correspondence also applies to models without translation invariance. By introducing structural disorder into the $C_4$-symmetric higher-order insulator, we show that the mode-shell correspondence remains a meaningful diagnostic in amorphous structures. The mode-shell correspondence generalizes to interacting states with a gapped bulk spectrum in the one-particle density matrix, providing a practical and diverse route to characterize higher-order topology from the quantum state itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03632 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A One-Particle Density Matrix Framework for Mode-Shell Correspondence: Characterizing Topology in Amorphous Higher-Order Topological Insulators Martínez, Miguel F. Jezequel, Lucien Bardarson, Jens H. Kvorning, Thomas Klein Hannukainen, Julia D. Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks We present a framework for characterizing higher-order topological phases directly from the one-particle density matrix, without any reference to an underlying Hamiltonian. Our approach extends the mode-shell correspondence, originally formulated for single-particle Hamiltonians, to Gaussian states subject to chiral constraints. In this correspondence, the mode index counts topological boundary modes, while the shell index quantifies the bulk topology in a region surrounding the modes, providing a bulk-boundary diagnostic. In one-dimensional topological insulators, the shell index reduces to the local chiral marker, recovering the winding number in the translation-invariant limit. We apply the mode-shell correspondence to a $C_4$-symmetric higher-order topological insulator with a chiral constraint and show that a fractional shell index implies that the higher-order phase is intrinsic. The one-particle density matrix is formulated in real space, so the mode-shell correspondence also applies to models without translation invariance. By introducing structural disorder into the $C_4$-symmetric higher-order insulator, we show that the mode-shell correspondence remains a meaningful diagnostic in amorphous structures. The mode-shell correspondence generalizes to interacting states with a gapped bulk spectrum in the one-particle density matrix, providing a practical and diverse route to characterize higher-order topology from the quantum state itself. |
| title | A One-Particle Density Matrix Framework for Mode-Shell Correspondence: Characterizing Topology in Amorphous Higher-Order Topological Insulators |
| topic | Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2509.03632 |