Inspired by recent experiments on graphene, we examine the non-dissipative viscoelastic response of anisotropic two-dimensional quantum systems. We pay particular attention to electron fluids with point group symmetries, and those with discrete translational symmetry. We start by extending the Kubo formalism for viscosity to systems with internal degrees of freedom and discrete translational symmetry, highlighting the importance of properly considering the role of internal angular momentum. We analyze the Hall components of the viscoelastic response tensor in systems with discrete point group symmetry, focusing on the hydrodynamic implications of the resulting forces. We show that though there are generally six Hall viscosities, there are only three independent contributions to the viscous force density in the bulk. To compute these coefficients, we develop a framework to consistently write down the long-wavelength stress tensor and viscosity for multi-component lattice systems. We apply our formalism to lattice and continuum models, including a lattice Chern insulator and anisotropic superfluid.

中文翻译：

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具有离散对称性的量子系统中的霍尔粘度：点群和晶格各向异性

受石墨烯最新实验的启发，我们研究了各向异性二维量子系统的非耗散粘弹性响应。我们特别注意具有点组对称性和具有离散平移对称性的电子流体。我们首先将粘度的久保形式主义扩展到具有内部自由度和离散平移对称性的系统，强调正确考虑内部角动量作用的重要性。我们分析了具有离散点群对称性的系统中粘弹性响应张量的霍尔分量，重点是合力的流体力学影响。我们显示，尽管通常有六种霍尔粘度，但是对于整体中的粘性力密度只有三项独立的贡献。要计算这些系数，我们开发了一个框架来一致记录多组分晶格系统的长波应力张量和粘度。我们将形式主义应用于晶格和连续体模型，包括晶格Chern绝缘体和各向异性超流体。