$p$-Body $\simeq$ Range $p-1$: Exact Order-Range Mapping and Dual-Unitarity

• URL: http://arxiv.org/abs/2607.16642v1
• Date: Sat, 18 Jul 2026 05:06:25 GMT
• Title: $p$-Body $\simeq$ Range $p-1$: Exact Order-Range Mapping and Dual-Unitarity
• Abstract summary: We study a periodically kicked version of a one-dimensional spin-$1/2$ Ising model with contiguous $p$-body interactions.<n>At specific interaction strengths, we establish an exact Floquet interaction $textitorder-range$ mapping.<n>We then determine exact entanglement dynamics of the $p$-body model for a class of solvable initial states at all times.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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