Numerical Study of Chiral Order in the Topological Phase of the Haldane-Heisenberg Model

Complex spin textures can emerge from nontrivial spin configurations within ferromagnetic phases, especially in systems exhibiting finite orbital magnetization. Even in the absence of explicit spin-orbit coupling, the interplay between spin chirality density and Berry-phase-induced orbital magnetization leads to effective chiral interactions that can significantly influence conventional Stoner ferromagnetism. In this work, we investigate an extension of the Haldane model on a honeycomb lattice, incorporating explicit spin degrees of freedom and nearest-neighbor ferromagnetic exchange interactions. This modified model allows us to explore the impact of chiral interactions on ferromagnetic order within a topologically nontrivial band structure. By employing Density Matrix Renormalization Group (DMRG) simulations, we systematically study the ground state properties of the system. We map out the parameter regimes that support both ferromagnetic and chiral orders, providing insights into the nature of the phase transitions and the competition between these orders. Our findings shed light on the interplay between topology, magnetism, and chiral interactions, contributing to the understanding of phase transitions in strongly correlated electron systems.