  We investigate a time-independent many-boson system, whose ground states are
quasi-degenerate and become infinitely degenerate in the thermodynamic limit.
Out of these quasi-degenerate ground states we construct a quantum state that
evolves in time with a period that is logarithmically proportional to the
number of particles, that is, T~logN. This boson system in such a state is a
quantum time crystal as it approaches the ground state in the thermodynamic
limit. The logarithmic dependence of its period on the total particle number N
makes it observable experimentally even for systems with very large number of
particles. Possible experimental proposals are discussed.
