  We report on discovery of a concentration of massive quiescent galaxies
located at z=4. The concentration is first identified using high-quality
photometric redshifts based on deep, mutli-band data in Subaru/XMM-Newton Deep
Field. Follow-up near-infrared spectroscopic observations with MOSFIRE on Keck
confirm a massive (~10^{11} Msun) quiescent galaxy at z=3.99. Our spectral
energy distribution (SED) analyses reveal that the galaxy experienced an
episode of starburst about 500 Myr prior to the observed epoch, followed by
rapid quenching. As its spectrum is sufficiently good to measure the stellar
velocity dispersion, we infer its dynamical mass and find that it is consistent
with its stellar mass. The galaxy is surrounded by 4 massive (>10^{10} Msun)
quiescent galaxies on a ~1 physical Mpc scale, all of which are consistent with
being located at the same redshift based on high-accuracy spectro-photometric
redshifts. This is likely a (proto-)cluster dominated by quiescent galaxies,
the first of the kind reported at such a high redshift as z=4. Interestingly,
it is in a large-scale structure revealed by spectroscopic redshifts from
VANDELS. Furthermore, it exhibits the red sequence, adding further support to
the physical concentration of the galaxies. We find no such concentration in
the Illustris-TNG300 simulation; it may be that the cluster is such a rare
system that the simulation box is not sufficiently large to reproduce it. The
total halo mass of the quiescent galaxies is ~10^{13} Msun, suggesting that
they form a group-sized halo once they collapse together. We discuss
implications of our findings for the quenching physics and conclude with future
prospects.
