  We investigate the phase diagram of the one-dimensional repulsive Hubbard
model with mass imbalance. Using DMRG, we show that this model has a triplet
paired phase (dubbed $\pi SG$) at generic fillings, consistent with previous
theoretical analysis. We study the topological aspect of $\pi SG$ phase,
determining long-range string orders and the "filling anomaly" which refers to
the relation among single particle gap, inversion symmetry and filling
imbalance for open chains. We also find, using DMRG, that at $1/3$ filling,
commensurate effects lead to two additional phases: a crystal phase and a trion
phase; we construct a description of these phases using Tomonaga-Luttinger
liquid theory.
