Study of Anderson localization in disordered system with bond breaking disorder

The dynamics and transport of a particle in condensed-matter systems can be described using a tight-binding Hamiltonian. In this work, we present a simple approach to investigate Anderson localization in a three-dimensional system with an off-diagonal disorder. We construct the tight-binding Hamiltonian for the system in which a single random energy is assigned to each lattice site, and the hopping integrals are restricted to nearest-neighbour sites only. We introduce bond-breaking disorder, where some hopping terms between sites are randomly weakened. We compute disorder-impacted density of states (DOS), the inverse participation ratio (IPR), and level statistics to identify the Anderson transition. Emergence of mobility edge has been seen while analysing inverse participation ratio with disorder. We address our problem in the thermodynamic limit by applying appropriate periodic boundary conditions and numerically demonstrate the existence of an Anderson localization transition.