We investigate the stability of topological phases in Kitaev-Heisenberg ladders under local charge fluctuations by studying the competition with itinerant electrons in a Hubbard model on a honeycomb ribbon geometry. We analyze the evolution of string order parameters, spin correlations, and charge fluctuations as functions of hopping amplitude and interaction strength in a half-filled band. Our results from density matrix renormalization group calculations show that increasing electron bandwidth progressively suppresses the topological phases, shifting and narrowing their stability regions in the phase diagram. We identify the critical values of hopping where string order vanishes and characterize the interplay between magnetic order and charge fluctuations. These findings provide insight into the robustness of topological phases against doping and charge dynamics, with implications for candidate Kitaev materials and engineered quantum systems.

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• Metal-insulator transition
• Quantum spin liquid
• Interfaces
• Mott insulators
• Strongly correlated systems
• Density matrix renormalization group
• Kitaev-Heisenberg model