  We use the density matrix renormalization group (DMRG) and a hard-core boson
map to investigate the quantum phase transitions present in the phase diagram
of the frustrated Heisenberg ladder in a magnetic field. The quantum bicritical
point is observed at the end of a first-order transition line, which is at the
meeting of the two second-order transition lines that bound the fully polarized
plateau. The characterization of the bicritical point was made using a
hard-core boson mapping of the low-energy excitations from the fully polarized
phase and through DMRG by studying the probability density of finding the rung
spins in a singlet or a triplet state with zero spin component along the
magnetic field. In particular, we give conditions for the exchange couplings
for the presence of the first-order transition line and the bicritical point in
the phase diagram. Moreover, we unveil the phase-separated states for
magnetization values inside the magnetization jump and, in particular, the
dependence on the system size of the energy curve as a function of
magnetization. Finite-size scaling analysis of the transverse spin correlation
functions has been used to estimate the critical points of the
Kosterlitz-Thouless transitions from the fractional magnetization plateau
$m=1/2$ to the respective gapless Luttinger liquid phases for some sets of
parameters.
