Chiral hinge modes in a dipole conserving lattice model

Recently, a "dipolar Chern Simons" response theory has been proposed to describe the topological responses of higher order topological insulators in 3D. Remarkably, this response theory also captures the essential features of certain classes of fractons. Here, we present a 3D interacting lattice model that realizes the dipolar Chern-Simons response theory, and hosts topologically protected chiral hinge modes. Interestingly, in the self-consistent mean field limit, this model maps onto a known non-interacting higher order topological insulator. We also relate the interacting 3D model to a 2D model with quantized quadrupole moment using dimensional reduction.