  We review recent works on the Monte Carlo simulations of dense two-color QCD
(QC$_2$D) by focusing on the phase diagram, the equation of state, and the
sound velocity at nonzero quark chemical potential. A possible upper bound of
the sound velocity is known as the conformal bound, namely, $c_s^2/c^2 \leq
1/3$. The sound velocity is below the bound at least in the case of
finite-temperature QCD. However, our recent work~\cite{Iida:2022hyy} shows the
breaking of this bound in dense QC$_2$D. This phenomenon was previously unknown
from any lattice calculations. We also discuss recent related works including
lattice studies on QCD at nonzero isospin chemical potential, some effective
model analyses, and an analysis based on recent neutron star observations.
These works also suggest the breaking of the conformal bound.
