  We revisit HHH model in [Phys. Rev. Lett. {\bf 101}, 031601 (2008)] and
extend the ansatz of matter fields to being of depending on a spatial dimension
except the holographic direction. Despite homogeneous solutions of ground and
excited states, especially for the excited states, there also exists solutions
where the translational invariance is broken. It is worth mentioning that no
periodic sources are assigned to the matter fields, so the translational
symmetry is broken spontaneously. We investigate how the new solutions and the
condensates of excited states develop with the change of temperature. Moreover,
since this kind of condensate will decrease at certain temperature and
eventually vanish at sufficiently low temperature, we also study the relation
between this interval and length of lattice. Besides, we compare the free
energies of non-translational invariant solutions and those of translational
invariance in the HHH model, and find that the free energies of the former
situations are lower.
