Itinerant carriers and topological phases in Kitaev-Heisenberg ladders 

The rich phase diagram of the Kitaev-Heisenberg (KH) system of spins on a honeycomb two-dimensional lattice has been the subject of much theoretical and experimental exploration in recent years.  Experimental systems are now poised to study the introduction of mobile carriers into such systems. We present results on the theoretical stability of topological phases in doped KH ladders by studying a Hubbard model with competing Heisenberg and Kitaev interactions on a honeycomb ribbon geometry. Using density-matrix renormalization group (DMRG) calculations, we analyze the evolution of string order parameters [1], spin correlations, and charge fluctuations as a function of the itinerant bandwidth (hopping amplitude) and interaction strength. The string order parameter is an especially sensitive indicator of the phase’s topological character. Our results show that increasing electron hopping progressively suppresses the topological phases, shifting and narrowing their stability regions in the KH parameter phase space. We identify critical hopping values at which string order vanishes and characterize the interplay between magnetic order and charge fluctuations. These findings provide insight into the robustness of topological spin phases against charge dynamics, with implications for candidate Kitaev materials and engineered quantum systems. 

[1] A. Catuneanu, E. S. Sørensen, and H.-Y. Kee, Phys. Rev. B 99, 195112 (2019).