A Single-Particle Diagnosis of an Interacting Topological Insulator

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.

Figures (9)

• Figure 1: Schematic of the SSH model with HK interactions. The two sites of the unit cell (blue) are labeled $A$ and $B$. Nearest neighbours separated by a distance $a$ are connected by intra- and inter-cell hopping amplitudes $v$ and $w$, respectively. The additional HK interaction of strength $U$ acting between all momentum states is illustrated by the orange wavy lines.
• Figure 2: Graphical representations of the spectral functions where blue(red) indicates a relation to the lower(upper) band in the non-interacting model. The chemical potential calculated from the filling is indicated with the dashed line. (a) BI+U. (b) HFMI. (c) QFMI.
• Figure 3: Schematic of the SSH model with HK interactions. Here, the sites (blue) of the unit cell (grey) are identified as A and B respectively. Each site is separated from its nearest neighbour by a distance $a$ with whom it shares an intra(inter)-cell hopping amplitude of $v$($w$). The additional HK interaction with uniform interaction strength $U$ for every site combination is represented by the orange wavy lines.
• Figure 4: Graphical representations of the spectral functions where blue(red) indicates a relation to the lower(upper) band in the non-interacting model. The chemical potential calculated from the filling is indicated with the dashed line. (a) BI+U. (b) HFMI. (c) QFMI.
• Figure 5: Effective winding number for the three phases studied in the model as a function of the inter-cell hopping $w$.