We investigate a rare instance of an exactly solvable nonequilibrium many-body problem. In particular, we derive an exact solution for the nonequilibrium dynamics of an initially localized single hole in a fully anisotropic antiferromagnetic Bethe lattice, described by the $t-J_z$ model. The solvability of the model relies on the fractal self-similarity of Bethe lattices, making it possible to compute the full motion of the hole as it moves through the lattice, as well as exactly characterizing the resulting effect on spin-spin correlation functions. We find that the hole remains bound to its initial position with large aperiodic oscillations in the hole density distribution. We track this back to the irregular pattern of the eigenenergies of the magnetic polaron ground state and string excitations, which we also determine exactly.

中文翻译：

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反铁磁 Bethe 晶格中的精确非平衡空穴动力学、磁极化子和弦激发

我们研究了一个完全可解的非平衡多体问题的罕见实例。特别是，我们推导出了完全各向异性反铁磁 Bethe 晶格中初始局部单孔的非平衡动力学的精确解，由$吨-{Ĵ}_z$模型。该模型的可解性依赖于 Bethe 晶格的分形自相似性，从而可以计算孔在穿过晶格时的完整运动，以及准确表征对自旋-自旋相关函数的影响。我们发现空穴仍然绑定在其初始位置，空穴密度分布存在较大的非周期性振荡。我们将其追溯到磁极化子基态和弦激发的本征能量的不规则模式，我们也准确地确定了这一模式。