Energy drag and shear viscosity in interacting quantum systems*

There has recently been a wave of interest in the hydrodynamical behavior of quantum many-body systems. Using `Coulomb drag’ physics as a guide, we discuss analogues of shear viscosity in quantum systems on discrete lattices. We argue that, although particle-hole symmetric materials have zero Coulomb drag, they nevertheless show a thermal equivalent in the form of drag between energy currents. Using a combination of perturbation theory and techniques from integrability, we give analytical predictions for this effect in coupled one-dimensional wires and compare them to DMRG studies on the Hubbard model. We comment on the generalization of these results to higher dimensional systems.