  We compute the matrix elements for elastic scattering of dark matter (DM)
particles off light nuclei ($^2$H, $^3$H, $^3$He, $^4$He and $^6$Li) using
quantum Monte Carlo methods. We focus on scalar-mediated DM-nucleus
interactions and use scalar currents obtained to next-to-leading order in
chiral effective theory. The nuclear ground states are obtained from a
phenomenological nuclear Hamiltonian that includes the Argonne $v_{18}$
two-body interaction and the three-body Urbana IX interaction. Within this
approach, we study the impact of one- and two-body currents and discuss the
size of nuclear uncertainties, including for the first time two-body effects in
$A=4$ and $A=6$ systems. Our results provide the nuclear structure input needed
to assess the sensitivity of future experimental searches of (light) dark
matter using light nuclei, such as $^3$He and $^4$He.
