For an interacting spatio-temporal lattice system we introduce a formal way of expressing multi-time correlation functions of local observables located at the same spatial point with a time state , i.e. a statistical distribution of configurations observed along a time lattice. Such a time state is defined with respect to a particular equilibrium state that is invariant under space and time translations. The concept is developed within the rule 54 reversible cellular automaton, for which we explicitly construct a matrix product form of the time state, with matrices that act on the three-dimensional auxiliary space. We use the matrix-product state to express equal-space time-dependent density-density correlation function, which, for special maximum-entropy values of equilibrium parameters, agrees with the previous results. Additionally, we obtain an explicit expression for the probabilities of observing all multi-time configurations, which enables us to study distrib...

中文翻译：

---

多次相关的矩阵乘积状态

对于一个相互作用的时空格网系统，我们引入了一种形式化的方式来表达位于同一空间点上具有时间状态的局部可观测对象的多时间相关函数，即沿时间格网观察到的配置的统计分布。相对于在空间和时间平移下不变的特定平衡状态来定义这种时间状态。这个概念是在规则54可逆细胞自动机中发展的，为此，我们明确构造了时间状态的矩阵乘积形式，其中矩阵作用于三维辅助空间。我们使用矩阵乘积状态来表示等时空相关的密度-密度相关函数，对于平衡参数的特殊最大熵值，该函数与先前的结果一致。另外，