We revisit HHH model [1] 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.

我们重新审视 HHH 模型 [1]，并将物质场的 ansatz 扩展到依赖于除全息方向之外的空间维度。尽管基态和激发态的齐次解，尤其是激发态，但也存在平移不变性被破坏的解。值得一提的是，物质场没有分配周期性源，因此平移对称性自发破缺。我们研究新的溶液和激发态凝聚如何随着温度的变化而发展。此外，由于这种凝聚体在一定温度下会减少，并最终在足够低的温度下消失，因此我们还研究了这个区间与晶格长度之间的关系。此外，我们还比较了HHH模型中非平移不变解和平移不变解的自由能，发现前一种情况的自由能较低。