Topological marker approach to an interacting Su-Schrieffer-Heeger model

TL;DR

This paper introduces a topological marker based on Green's functions to identify topological phases in an interacting SSH model, successfully distinguishing phases and phase transitions despite interactions.

Contribution

It generalizes the topological marker to interacting systems using Green's functions, enabling phase detection in models with interactions and symmetry considerations.

Findings

Marker remains finite in topological phase with interactions

Marker converges to zero in trivial phase in thermodynamic limit

Successfully detects interaction-driven topological phase transitions

Abstract

The topological properties of the Su-Schrieffer-Heeger (SSH) model in the presence of nearest-neighbor interaction are investigated by means of a topological marker, generalized from a noninteracting one by utilizing the single-particle Green's function of the many-body ground state. We find that despite the marker not being perfectly quantized in the presence of interactions, it always remains finite in the topologically nontrivial phase while converging to zero in the trivial phase when approaching the thermodynamic limit, and hence correctly judges the topological phases in the presence of interactions. The marker also correctly captures the interaction-driven, second-order phase transitions between a topological phase and a Landau-ordered phase, which is a charge density wave order in our model with a local order parameter, as confirmed by the calculation of entanglement entropy and the many-body Zak phase. Our work thus points to the possibility of generalizing topological markers to interacting systems through Green's function, which may be feasible for topological insulators in any dimension and symmetry class.