  Periodically driven quantum systems manifest various non-equilibrium features
which are absent at equilibrium. For example, discrete time-translation
symmetry can be broken in periodically driven quantum systems leading to an
exotic phase of matter, called discrete time crystal(DTC). For open quantum
systems, previous studies showed that DTC can be found only when there exists a
meta-stable state in the undriven system. However, by investigating the
simplest Bose-Hubbard model with dissipation and time periodically tunneling,
we find in this paper that a $2T$ DTC can appear even when the meta-stable
state is absent in the undriven system. This observation extends the
understanding of DTC and shed more light on the physics behind the DTC.
Besides, by the detailed analysis of simplest two-sites model, we show further
that the two-sites model can be used as basic building blocks to construct
large rings in which a $nT$ DTC might appear. These results might find
applications into engineering exotic phases in driven open quantum systems.
