  We study the effect of quantum geometry on the many-body ground state of
one-dimensional interacting bosonic systems. We find that the Drude weight is
given by the sum of the kinetic energy and a term proportional to the many-body
quantum metric of the ground state. Notably, the many-body quantum metric
determines the upper bound of the Drude weight. We validate our results on the
Creutz ladder, a flat band model, using exact diagonalization at half and unit
densities. Our work sheds light on the importance of the many-body quantum
geometry in one-dimensional interacting bosonic systems.
