Lieb-Robinson and related bounds set an upper limit on the speed at which information propagates in nonrelativistic quantum systems. Experimentally, light-cone-like spreading has been observed for correlations in the Bose-Hubbard model (BHM) after a quantum quench. Using a two-particle irreducible (2PI) strong-coupling approach to out-of-equilibrium dynamics in the BHM we calculate both the group and phase velocities for the spreading of single-particle correlations in one, two, and three dimensions as a function of interaction strength. Our results are in quantitative agreement with measurements of the speed of spreading of single-particle correlations in both the one- and two-dimensional BHM realized with ultracold atoms. They also are consistent with the claim that the phase velocity rather than the group velocity was observed in recent experiments in two dimensions. We demonstrate that there can be large differences between the phase and group velocities for the spreading of correlations and explore how the anisotropy in the velocity varies across the phase diagram of the BHM. Our results establish the 2PI strong-coupling approach as a powerful tool to study out-of-equilibrium dynamics in the BHM in dimensions greater than one.

中文翻译：

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在Bose-Hubbard模型的Mott相中相关展开的相速度和群速度大于一

Lieb-Robinson及其相关范围为信息在非相对论量子系统中的传播速度设定了上限。实验上，在量子猝灭后，在Bose-Hubbard模型（BHM）中已观察到类似光锥的传播相关性。使用两粒子不可约（2PI）强耦合方法解决BHM中的不平衡动力学问题，我们计算了单粒子相关性在一维，二维和三维中的扩散函数的群速度和相速度互动强度。我们的结果与通过超冷原子实现的一维和二维BHM中单粒子相关性扩散速度的测量结果在定量上吻合。它们也与在最近的二维实验中观察到相速度而不是群速度的说法是一致的。我们证明了在相速度和群速度之间可能存在较大的差异，以扩展相关性，并探讨了速度各向异性在BHM的整个相图中如何变化。我们的结果将2PI强耦合方法确立为研究BHM中尺寸大于1的平衡失衡动力学的有力工具。