  A quantum phase transition is a dramatic event marked by large spatial and
temporal fluctuations, where one phase of matter with its ground state and
tower of excitations reorganizes into a completely different phase. We provide
new insight into the disorder-driven superconductor-insulator transition (SIT)
in two dimensions, a problem of great theoretical and experimental interest,
with the dynamical conductivity \sigma(\omega) and the bosonic (pair) spectral
function P(\omega) calculated from quantum Monte Carlo simulations. We identify
characteristic energy scales in the superconducting and insulating phases that
vanish at the transition due to enhanced quantum fluctuations, despite the
persistence of a robust fermionic gap across the SIT. Disorder leads to
enhanced absorption in \sigma(\omega) at low frequencies compared to the SIT in
a clean system. Disorder also expands the quantum critical region, due to a
change in the universality class, with an underlying T=0 critical point with a
finite low-frequency conductivity.
