  We study the magnetic field dependence of the ground state of $S=1/2$
$J_1$-$J_2$ Heisenberg model on the square lattice by the DMRG method with the
sine-square deformation. We obtain 8 different phases including plaquette
valence-bond crystal with a finite spin gap, transverse N$\acute{\rm e}$el,
transverse stripe, 1/2 magnetization plateau with up-up-up-down (uuud), and
three new phases we named Y-like, V-like, and $\Psi$ phases around $J_2/J_1$
=0.55-0.6 depending on the magnetic field. The phase transitions to uuud and
Y-like states from transverse N$\acute{\rm e}$el (at $J_2/J_1$ = 0.55) and
stripe (at $J_2/J_1$ = 0.6) states are discontinuous, as in the case of
spin-flop.
