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The presence of symmetries in a closed many-body quantum system results inintegrability. For such integrable systems, complete thermalization does notoccur. As a result, the system remains non-ergodic. On the other hand, a set ofnon-interacting atoms connected to a regular bosonic bath thermalizes. Here, weshow that such atoms in a spatially-correlated thermal bath can show both thebehavior depending on the temperature. At zero temperature, the bath has alarge correlation length, and hence it acts as a common environment. In thiscondition, a set of weak symmetries exist, which prevent thermalization. Thesystem undergoes a symmetry-broken dissipative phase transition of the firstorder as the temperature rises above zero.

Dissipative phase transition in a spatially-correlated bosonic bath