Influence of local connectivity on the Anderson transition beyond bandwidth broadening
Phys. Rev. B 114, 134201 – Published 3 September, 2026
DOI: https://doi.org/10.1103/7wty-9cpy
Abstract
We investigate the Anderson metal-insulator transition in three-dimensional lattices with systematically enhanced local connectivity. By introducing modified cubic lattices with seven- and eight-nearest neighbors (7NN and 8NN) per site, we tune the coordination number in a controlled manner while preserving dimensionality, symmetry class, hopping amplitude, and disorder statistics. Using exact diagonalization of a disordered tight-binding Hamiltonian, we characterize localization through complementary spectral and wave-function diagnostics, including level-spacing statistics and inverse participation ratio (IPR) scaling. Finite-size scaling analyses reveal disorder-driven metal-insulator transitions with critical disorder strengths that increase monotonically from the conventional simple cubic lattice to the 7NN and 8NN realizations. Remarkably, this enhancement cannot be explained by bandwidth broadening alone: The normalized ratio increases systematically with coordination number, demonstrating that local connectivity influences localization beyond simple spectral rescaling. Consistent with this interpretation, the modified 8NN lattice exhibits a critical disorder strength nearly identical to that of the conventional body-centered cubic lattice despite its fundamentally different connectivity geometry, suggesting that local connectivity can play an important role in determining the localization threshold, alongside bandwidth and detailed hopping geometry. Energy-resolved IPR maps further reveal mobility-edge-type behavior, showing that enhanced connectivity systematically enlarges the extended region of the spectrum and shifts localization crossover boundaries to higher disorder strengths. Despite these substantial changes in localization thresholds, the correlation-length exponent and multifractal properties remain consistent with the three-dimensional orthogonal universality class. These results demonstrate that controlled modification of local connectivity can provide a powerful route for tuning localization behavior in disordered quantum systems while preserving universal criticality.
