  This study investigates the entanglement properties of disordered free
fermion systems undergoing an Anderson phase transition from a delocalized to a
localized phase. The entanglement entropy is employed to quantify the degree of
entanglement, with the system randomly divided into two subsystems. To explore
this phenomenon, one-dimensional tight-binding fermion models and Anderson
models in one, two, and three dimensions are utilized. Comprehensive numerical
calculations reveal that the entanglement entropy, determined using random
bi-partitioning, follows a volume-law scaling in both the delocalized and
localized phases, expressed as $EE \propto L^D$, where $D$ represents the
dimension of the system. Furthermore, the role of short and long-range
correlations in the entanglement entropy and the impact of the distribution of
subsystem sites are analyzed.
