  Disorder is a key factor influencing the behavior of condensed states of
matter, however the true extent of its impact is generally difficult to
determine due to the prominent roles played by quantum interference,
entanglement between spin and orbital degrees of freedom and proximity to
quantum critical points. Here we show that the one-particle disorder
self-energy -- a direct probe of the renormalization of low-energy excitations
due to defects and impurities distributed randomly in a crystal -- can be
obtained by means of unbiased spectral expansions of lattice Green's functions
in a computationally expedient manner. Our scheme provides a powerful framework
to map out the frequency and wavevector dependence of electronic excitations in
unprecedented large tight-binding systems, up to $10^9$ orbitals, with energy
resolution only limited by the mean level spacing. We demonstrate the
versatility of our approach in 3 distinct problems: (i) the Gade singularity in
honeycomb layers with dilute topological defects; (ii) the rich landscape of
impurity resonances in a spin-orbit-coupled ferromagnet; and (iii) the
tailoring of emergent s-wave and p-wave superconducting phases in graphene via
atomic defects. These examples reveal rich features in the disorder self-energy
$\Sigma_{\textrm{dis}}(\mathbf{k},\omega)$ that are absent from the
self-consistent T-matrix approach and other common approximation schemes, which
include regimes of nontrivial wavevector dependence and anomalous dependence
upon the impurity concentration. Our study unravels puzzling, and so far
largely inaccessible, manifestations of strong nonperturbative quantum
interference effects in quantum materials and disordered phases of matter.
