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Inspired by recent experiments on graphene, we examine the non-dissipativeviscoelastic response of anisotropic two-dimensional quantum systems. We payparticular attention to electron fluids with point group symmetries, and thosewith discrete translational symmetry. We start by extending the Kubo formalismfor viscosity to systems with internal degrees of freedom and discretetranslational symmetry, highlighting the importance of properly considering therole of internal angular momentum. We analyze the Hall components of theviscoelastic response tensor in systems with discrete point group symmetry,focusing on the hydrodynamic implications of the resulting forces. We show thatthough there are generally six Hall viscosities, there are only threeindependent contributions to the viscous force density in the bulk. To computethese coefficients, we develop a framework to consistently write down thelong-wavelength stress tensor and viscosity for multi-component latticesystems. We apply our formalism to lattice and continuum models, including alattice Chern insulator and anisotropic superfluid.

Hall viscosity in quantum systems with discrete symmetry: point group and lattice anisotropy