# Statistical Analysis of the Chern Number in the Interacting Haldane-Hubbard Model

## TL;DR

This paper investigates how local and non-local self-energy contributions affect the robustness of the Chern number in the interacting Haldane-Hubbard model, providing a statistical method to estimate uncertainty in topological invariants.

## Contribution

It introduces a statistical analysis to quantify the impact of momentum dependence in the self-energy on the Chern number in many-body systems.

## Key findings

- Local self-energy captures the qualitative topological phase diagram.
- Momentum dependence refines the phase transition location.
- A stochastic upper bound estimates Chern number uncertainty.

## Abstract

In the context of many-body interacting systems described by a topological Hamiltonian, we investigate the robustness of the Chern number with respect to different sources of error in the self-energy. In particular, we analyze the importance of non-local (momentum dependent) vs. local contributions to the self-energy and show that the local self-energy provides a qualitative description of the topological phase diagrams of many-body interacting systems, whereas the explicit momentum-dependence constitutes a correction to the exact location of the phase transition. For the latter, we propose a statistical analysis, on the basis of which we develop a stochastic upper bound for the uncertainty of the Chern number as a function of the amount of momentum-dependence of the self-energy. We apply this analysis to the Haldane-Hubbard model and discuss the implications of our results for a general class of many-body interacting systems.