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arXiv:2603.11879

A Single-Particle Diagnosis of an Interacting Topological Insulator

Théo N. Dionne, Maia G. Vergniory

Published Mar 12, 2026• 0 citations
arXivHTMLPDF

Abstract

Understanding how topology survives in strongly correlated systems remains a central challenge, as most topological diagnostics rely on non-interacting band structures. Here we present a framework to characterize interacting topological phases within an effective single-particle description derived from the single-particle Green's function. Using the Su-Schrieffer-Heeger model with Hatsugai-Kohmoto interactions as an analytically tractable example, we construct the one-body reduced density matrix from the Green's function and use it to define an effective winding number together with quantum volume, a measurement of state geometry. These quantities allow us to distinguish three insulating phases including correlated Mott states directly from single-particle observables. Our results show that interacting topology can be interpreted in terms of the spectral weight distribution of single-particle excitations, providing an intuitive and computationally accessible route to diagnose topological phases in correlated systems. This approach is compatible with modern many-body simulation techniques and opens a pathway toward the identification of interacting topological materials.

DOI
10.48550/arxiv.2603.11879

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Understanding how topology survives in strongly correlated systems remains a central challenge, as most topological diagnostics rely on non-interacting band structures. Here we present a framework to characterize interacting topological phases within an effective single-particle description derived from the single-particle Green's function. Using the Su-Schrieffer-Heeger model with Hatsugai-Kohmoto interactions as an analytically tractable example, we construct the one-body reduced density matrix from the Green's function and use it to define an effective winding number together with quantum volume, a measurement of state geometry. These quantities allow us to distinguish three insulating phases including correlated Mott states directly from single-particle observables. Our results show that interacting topology can be interpreted in terms of the spectral weight distribution of single-particle excitations, providing an intuitive and computationally accessible route to diagnose topological phases in correlated systems. This approach is compatible with modern many-body simulation techniques and opens a pathway toward the identification of interacting topological materials.
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We study the effects of electron-electron interactions on the charge excitation spectrum of the spinful Su-Schrieffer-Heeger (SSH) model, a prototype of a one-dimensional bulk obstructed topological insulator. In view of recent progress in the fabrication of dopant-based quantum simulators we focus on experimentally detectable signatures of interacting topology in finite lattices. To this end we use Lanczos-based exact diagonalization to calculate the single-particle spectral function in real space which generalizes the local density of states to interacting systems. Its spatial and spectral resolution allows for the direct investigation and identification of edge states. By studying the noninteracting limit, we demonstrate that the topological in-gap states on the boundary are robust against both finite-size effects as well as random bond and onsite disorder which suggests the feasibility of simulating the SSH model in engineered dopant arrays in silicon. While edge excitations become zero-energy spinlike for any finite interaction strength, our analysis of the spectral function shows that the single-particle charge excitations are gapped out on the boundary. Despite the loss of topological protection, we find that these edge excitations are quasiparticlelike as long as they remain within the bulk gap. Above a critical interaction strength of ${U}_{c}\ensuremath{\approx}5t$ these quasiparticles on the boundary lose their coherence which is explained by the merging of edge and bulk states. This is in contrast to the many-body edge excitations which survive the limit of strong coupling, as established in the literature. Our findings show that for moderate repulsive interactions the nontrivial phase of the interacting SSH model can be detected through remnant signatures of topological single-particle states using single-particle local measurement techniques such as scanning tunneling spectroscopy.