  The decreasing proton and charge densities from around 5.0 fm towards the
center of $^{204, 206}$Hg are investigated by a covariant density functional
theory at the beyond mean-field level.The charge-density difference between
$^{208}$Pb and $^{204}$Hg is improved significantly and a central depression is
still visible in the ground-state density of $^{204, 206}$Hg when the dynamic
correlations associated with symmetry restoration and shape mixing are taken
into account. For the $0_2^+$ and $2_1^+$ excited states of $^{204, 206}$Hg,
their densities remain decreasing from 5.0 fm to around 2.0 fm, but become flat
in the interior region. The results show that the bubble structure in $^{204,
206}$Hg within 2.0 fm is mainly attributed to the quantum effect, while that
beyond 2.0 fm is formed by the Coulomb repulsion.
