  In this work an exactly solvable model of N two-level systems interacting
with a single bosonic dephasing reservoir is considered to unravel the role
played by collective non-Markovian dephasing. We show that phase estimation
with entangled states for this model can exceed the standard quantum limit and
demonstrate Heisenberg scaling with the number of atoms for an arbitrary
temperature. For a certain class of reservoir densities of states decoherence
can be suppressed in the limit of large number of atoms and the Heisenberg
limit can be restored for arbitrary interrogation times. We identify the second
class of densities when the Heisenberg scaling can be restored for any finite
interrogation time. We also find the third class of densities when the standard
quantum limit can be exceeded only on the initial stage of dynamics in the
Zeno-regime.
