A Single-Particle Diagnosis of an Interacting Topological Insulator

TL;DR

This paper introduces a method to diagnose topological phases in strongly correlated systems using an effective single-particle Green's function approach, enabling identification of topological states in interacting materials.

Contribution

It develops a framework to characterize interacting topological phases via single-particle observables derived from Green's functions, applicable to correlated systems.

Findings

Distinguished three insulating phases including Mott states using single-particle measures.

Defined an effective winding number and quantum volume from Green's function.

Demonstrated the approach on the Su-Schrieffer-Heeger model with interactions.

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.