Topological order in the Haldane model with spin-spin on-site interactions

TL;DR

This paper investigates the robustness of topological phases in a generalized Haldane model with spin-spin interactions, using advanced computational methods and proposing experimental implementation with ultracold atoms.

Contribution

It introduces a mean-field and matrix product state approach to study topological order in an interacting Haldane model and demonstrates the persistence of topological phases under interactions.

Findings

Topological phases survive interactions comparable to kinetic energy.

Mean-field approach effectively captures long-range correlations.

Proposed ultracold atom experiments can detect topological phases.

Abstract

Ultracold atom experiments allow the study of topological insulators, such as the noninteracting Haldane model. In this work we study a generalization of the Haldane model with spin-spin on-site interactions that can be implemented on such experiments. We focus on measuring the winding number, a topological invariant, of the ground state, which we compute using a mean-field calculation that effectively captures long range correlations and a matrix product state computation in a lattice with 64 sites. Our main result is that we show how the topological phases present in the noninteracting model survive until the interactions are comparable to the kinetic energy. We also demonstrate the accuracy of our mean-field approach in efficiently capturing long-range correlations. Based on state-of-the-art ultracold atom experiments, we propose an implementation of our model that can give information about the topological phases.