  We performed a systematic spectroscopic observation of a protocluster at
$z=6.01$ in the Subaru Deep Field. We took spectroscopy for all 53 $i'$-dropout
galaxies down to $z'=27.09\,\mathrm{mag}$ in/around the protocluster region.
From these observations, we confirmed that 28 galaxies are at $z\sim6$, of
which ten are clustered in a narrow redshift range of $\Delta z<0.06$. To trace
the evolution of this primordial structure, we applied the same $i'$-dropout
selection and the same overdensity measurements used in the observations to a
semi-analytic model built upon the Millennium Simulation. We obtain a relation
between the significance of overdensities observed at $z\sim6$ and the
predicted dark matter halo mass at $z=0$. This protocluster with $6\sigma$
overdensity is expected to grow into a galaxy cluster with a mass of
$\sim5\times10^{14}\,\mathrm{M_\odot}$ at $z=0$. Ten galaxies within
$10\,\mathrm{comoving\>Mpc}$ of the overdense region can, with more than an 80%
probability, merge into a single dark matter halo by $z=0$. No significant
differences appeared in UV and Ly$\alpha$ luminosities between the protocluster
and field galaxies, suggesting that this protocluster is still in the early
phase of cluster formation before the onset of any obvious environmental
effects. However, further observations are required to study other properties,
such as stellar mass, dust, and age. We do find that galaxies tend to be in
close pairs in this protocluster. These pair-like subgroups will coalesce into
a single halo and grow into a more massive structure. We may witness an onset
of cluster formation at $z\sim6$ toward a cluster as seen in local universe.
