  Anderson Orthogonality (AO) refers to the fact that the ground states of two
Fermi seas that experience different local scattering potentials, say |G_I> and
|G_F>, become orthogonal in the thermodynamic limit of large particle number N,
in that |<G_I|G_F>| ~ N^(- Delta_AO^2 /2) for N->infinity. We show that the
numerical renormalization group (NRG) offers a simple and precise way to
calculate the exponent Delta_AO: the overlap, calculated as function of Wilson
chain length k, decays exponentially, ~ exp(-k alpha), and Delta_AO can be
extracted directly from the exponent alpha. The results for Delta_AO so
obtained are consistent (with relative errors typically smaller than 1%) with
two other related quantities that compare how ground state properties change
upon switching from |G_I> to |G_F>: the difference in scattering phase shifts
at the Fermi energy, and the displaced charge flowing in from infinity. We
illustrate this for several nontrivial interacting models, including systems
that exhibit population switching.
