标题： 钟模型中的弗洛凯时间晶体 显示英文标题

标题： Floquet time crystals in clock models

摘要： 我们构建了一类基于$\mathbb{Z}_n$时钟变量的周期为$n$的离散时间晶体类，适用于所有整数$n$。我们考虑两种系统类别，这种现象会发生，即具有短程相互作用的无序模型和全连接模型。在短程模型的情况下，我们提供了对通用$n$的时间晶体相的完整分类。对于$n=3$和$n=4$的具体案例，我们通过精确对角化详细研究了动力学。在两种情况下，通过对外尔谱的广泛分析，我们能够完全映射相图。在无限程模型的情况下，将其映射到有效玻色哈密顿量允许我们研究向热力学极限的标度。 在对问题的一般讨论之后，我们关注$n=3$和$n=4$，它们是普遍行为的代表性例子。值得注意的是，对于$n=4$，我们发现了晶体到晶体的新转变的明确证据，介于周期$n$倍增和周期$n/2$倍增之间。 显示英文摘要

摘要： We construct a class of period-$n$-tupling discrete time crystals based on $\mathbb{Z}_n$ clock variables, for all the integers $n$. We consider two classes of systems where this phenomenology occurs, disordered models with short-range interactions and fully connected models. In the case of short-range models we provide a complete classification of time-crystal phases for generic $n$. For the specific cases of $n=3$ and $n=4$ we study in details the dynamics by means of exact diagonalisation. In both cases, through an extensive analysis of the Floquet spectrum, we are able to fully map the phase diagram. In the case of infinite-range models, the mapping onto an effective bosonic Hamiltonian allows us to investigate the scaling to the thermodynamic limit. After a general discussion of the problem, we focus on $n=3$ and $n=4$, representative examples of the generic behaviour. Remarkably, for $n=4$ we find clear evidence of a new crystal-to-crystal transition between period $n$-tupling and period $n/2$-tupling.