  We study hardcore bosons on a triangular ladder at half filling in the
presence of a frustrating hopping term and a competing nearest neighbor
repulsion $V$ which promotes crystallization. Using the finite-size
density-matrix renormalization group method, we obtain the phase diagram which
contains three phases: a uniform superfluid (SF), an insulating charge density
wave (CDW) crystal and a bond ordered insulator (BO). We find that the
transitions from SF to CDW and SF to BO are continuous in nature, with critical
exponents varying continously along the phase boundaries, while the transition
from CDW to BO is found to be first order. The phase diagram is also shown to
contain an exactly solvable Majumdar Ghosh point, and re-entrant SF to CDW
phase transitions.
