Quantum Dualities and Quantum Anomalous Hall Phases with Arbitrary Large Chern Numbers

Quantum duality is a far reaching concept in contemporary theoretical physics. In the present paper, we reveal the quantum dualities in quantum anomalous Hall (QAH) phases through concrete two bands Hamiltonian models. Our models can realize QAH phases with arbitrary large Chern numbers. In real materials these models may be realized by stacked $n$ layer systems of $c_1=1$ QAH insulators. The topological phase transitions that can change the Chern numbers are studied. And we investigate the gapless edge modes of our models in details, and find a new mechanism for the bulk boundary correspondence.