In order to prepare for the introduction of dynamical many-body and, eventually, field theoretical models, we show here that quantum mechanical exchange interactions in a three-spin chain can emerge from the deterministic dynamics of three classical Ising spins. States of the latter form an ontological basis, which will be discussed with reference to the ontology proposed in the Cellular Automaton Interpretation of Quantum Mechanics by ’t[Formula: see text]Hooft. Our result illustrates a new Baker–Campbell–Hausdorff (BCH) formula with terminating series expansion.

中文翻译：

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来自经典比特排列的量子比特交换相互作用

为了准备引入动态多体模型，最终引入场理论模型，我们在此展示了三自旋链中的量子力学交换相互作用可以从三个经典伊辛自旋的确定性动力学中出现。后者的状态构成了本体论基础，将参考't[公式：见正文]Hooft在量子力学的元胞自动机解释中提出的本体论进行讨论。我们的结果说明了具有终止级数展开的新贝克-坎贝尔-豪斯多夫 (BCH) 公式。