  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 $\pi \mathrm{SG}$) at generic fillings, consistent with
previous theoretical analysis. We study the topological aspect of $\pi
\mathrm{SG}$ phase, determining long-range string orders and the filling
anomaly which refers to the relation among the 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.
