  The presence of symmetries in a closed many-body quantum system results in
integrability. For such integrable systems, complete thermalization does not
occur. As a result, the system remains non-ergodic. On the other hand, a set of
non-interacting atoms connected to a regular bosonic bath thermalizes. Here, we
show that such atoms in a spatially-correlated thermal bath can show both the
behavior depending on the temperature. At zero temperature, the bath has a
large correlation length, and hence it acts as a common environment. In this
condition, a set of weak symmetries exist, which prevent thermalization. The
system undergoes a symmetry-broken dissipative phase transition of the first
order as the temperature rises above zero.
