  We present a systematic study of the role of Anderson orthogonality for the
dynamics after a quantum quench in quantum impurity models, using the numerical
renormalization group. As shown by Anderson in 1967, the scattering phase
shifts of the single-particle wave functions constituting the Fermi sea have to
adjust in response to the sudden change in the local parameters of the
Hamiltonian, causing the initial and final ground states to be orthogonal. This
so-called Anderson orthogonality catastrophe also influences dynamical
properties, such as spectral functions. Their low-frequency behaviour shows
nontrivial power laws, with exponents that can be understood using a
generalization of simple arguments introduced by Hopfield and others for the
X-ray edge singularity problem. The goal of this work is to formulate these
generalized rules, as well as to numerically illustrate them for quantum
quenches in impurity models involving local interactions. As a simple yet
instructive example, we use the interacting resonant level model as testing
ground for our generalized Hopfield rule. We then analyse a model exhibiting
population switching between two dot levels as a function of gate voltage,
probed by a local Coulomb interaction with an additional lead serving as charge
sensor. We confirm a recent prediction that charge sensing can induce a quantum
phase transition for this system, causing the population switch to become
abrupt. We elucidate the role of Anderson orthogonality for this effect by
explicitly calculating the relevant orthogonality exponents.
