$p$-体 $\simeq$ 范围 $p - 1$：精确的阶-范围映射与对偶酉性
$p$-Body $\simeq$ Range $p-1$: Exact Order-Range Mapping and Dual-Unitarity
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中文总结 AI 辅助
研究具有连续 $p$-体相互作用的一维自旋-1/2 伊辛模型的周期性驱动版本，通过建立精确的弗洛凯相互作用阶-范围映射，得到对偶酉模型，确定纠缠动力学，并用实例说明映射结构，为构建和研究 $p$-体对偶酉弗洛凯模型提供途径。
中文摘要 AI 辅助
我们引入并研究了具有连续 $p$-体相互作用的一维自旋-1/2 伊辛模型的周期性驱动版本。在模型的特定相互作用强度下，我们建立了精确的弗洛凯相互作用阶-范围映射：$p$-体伊辛模型的弗洛凯演化算符精确映射到具有最大范围 $p - 1$ 和精确确定耦合的两体伊辛模型。进一步调整驱动强度后，映射模型变为对偶酉的，从而提供了一族明确的 $p$-体对偶酉模型。然后我们确定了 $p$-体模型对于一类可解初始态在所有时刻的精确纠缠动力学。我们还用 $p = 3$ 的最小例子说明了阶-范围映射可能出现的确切非平凡结构，并将其推广到所有奇数 $p$。这些发现为构建和研究 $p$-体对偶酉弗洛凯模型提供了一条系统途径。
英文摘要
We introduce and study a periodically kicked version of a one-dimensional spin-$1/2$ Ising model with contiguous $p$-body interactions. At specific interaction strengths of the model, we establish an exact Floquet interaction $\textit{order-range}$ mapping: the Floquet evolution operator of the $p$-body Ising model is exactly mapped to a two body Ising model with interactions having maximum range $p-1$ and exactly determined couplings. Upon further tuning the kicking strength, the mapped model becomes dual-unitary, thus providing an explicit family of $p$-body dual unitary models. We then determine exact entanglement dynamics of the $p$-body model for a class of solvable initial states at all times. We further illustrate the nontrivial structures that can emerge from the $\textit{order-range}$ mapping using a minimal example of $p=3$ and generalize it for all odd $p$. These findings provide a systematic route to constructing and studying $p$-body dual-unitary Floquet models.
