  We study entanglement Hamiltonian (EH) associated with the reduced density
matrix of free fermion models in delocalized-localized Anderson phase
transition. We show numerically that the structure of the EH matrix
differentiates the delocalized from the localizedphase. In the delocalized
phase, EH becomes a long-range Hamiltonian but is short-range in the localized
phase, no matter what the configuration of the system's Hamiltonian is (whether
it is long or short range). With this view, we introduce the entanglement
conductance (EC), which quantifies how much EH is long-range and propose it as
an alternative quantity to measure entanglement in the Anderson phase
transition, by which we locate the phase transition point of some
one-dimensional free fermion models; and also by applying the finite size
method to the EC, we find three-dimensional Anderson phase transition critical
disorder strength.
