We have developed a formalism that allows the study of correlations in space and time in the Bose–Hubbard model, both in equilibrium and out of equilibrium. We obtain a two-particle irreducible effective action in the contour-time formalism that allows us to obtain equations of motion for the superfluid order parameter and two-point correlation functions. We use these equations to calculate equilibrium phase diagrams that are significant improvements on mean field theory and apply them to study the spreading of correlations after a quench in the Mott insulator phase. We study the single-particle density matrix and find velocities for the spreading of correlations in one, two and three dimensions. We discuss the prospects of generalizing this approach to study the disordered Bose–Hubbard model.

中文翻译：

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Bose-Hubbard 模型中相关性的时空传播

我们开发了一种形式主义，允许研究 Bose-Hubbard 模型中空间和时间的相关性，无论是在平衡状态还是非平衡状态。我们在轮廓时间形式中获得了一个两粒子不可约的有效作用，它使我们能够获得超流体阶参数和两点相关函数的运动方程。我们使用这些方程来计算平衡相图，这些图是平均场理论的重大改进，并将它们应用于研究莫特绝缘体相失超后相关性的扩展。我们研究单粒子密度矩阵并找到相关性在一维、二维和三个维度上的传播速度。我们讨论了将这种方法推广到研究无序 Bose-Hubbard 模型的前景。