We introduce a class of integrable dynamical systems of interacting classical matrix-valued fields propagating on a discrete space-time lattice, realized as many-body circuits built from elementary symplectic two-body maps. The models provide an efficient integrable Trotterization of non-relativistic $\sigma$-models with complex Grassmannian manifolds as target spaces, including, as special cases, the higher-rank analogues of the Landau-Lifshitz field theory on complex projective spaces. As an application, we study transport of Noether charges in canonical local equilibrium states. We find a clear signature of superdiffusive behavior in the Kardar-Parisi-Zhang universality class, irrespectively of the chosen underlying global unitary symmetry group and the quotient structure of the compact phase space, providing a strong indication of superuniversal physics.

中文翻译：

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离散时空中的可积矩阵模型

我们介绍了一类在离散时空晶格上传播的，相互作用的经典矩阵值场的可积动力学系统，实现为由基本辛两体图构建的多体电路。这些模型提供了以复杂格拉斯曼流形为目标空间的非相对论性$ \ sigma $模型的有效可积Trotterization，在特殊情况下，包括复杂投影空间上Landau-Lifshitz场论的上等类似物。作为应用，我们研究了规范局部平衡态下Noether电荷的传输。我们发现在Kardar-Parisi-Zhang普适性类中的超扩散行为具有明显的特征，而与所选的基础整体unit对称群和紧致相空间的商结构无关，