Generalized dynamical cluster theory for off-diagonal disorder

We present a generalized dynamical cluster theory for addressing the cluster effects of off -diagonal disorder. In this work, we introduce an extended local degree of freedom, namely the coupling space, to encapsulate the off -diagonal disorder in an auxiliary medium, and to form a cluster coupling space so that each site of the cluster can be homogenously handled. Within the cluster coupling space, the self -consistent auxiliary dynamical cluster approximation (ADCA) with full symmetry of the lattice is developed to treat the diagonal and off -diagonal disorders on an equal footing. ADCA recovers the coherent -potential approximation at the single -site limit and the dynamical cluster approximation for diagonal -only disorder. Especially for the disordered vibrational system, ADCA conserves the force -constant sum rule. As important tests, we apply ADCA to the one- and three-dimensional disordered lattices, and we find that the ADCA density of state results with appropriate cluster size are in very good agreement with the exact and supercell calculations, especially for the localized defect modes. Moreover, the important interplay of mass and force -constant disorders is revealed by comparing the geometrically and arithmetically averaged density of states calculated by ADCA, presenting both effects of significantly enhanced localization and delocalization. The development of ADCA provides an effective approach for simulating both diagonal and off -diagonal disorders in materials.