  A perturbative renormalization group (RG) scheme for light-front Hamiltonian
is formulated on the basis of the Bloch-Horowitz effective Hamiltonian, and
applied to the simplest $\phi^4$ model with spontaneous breaking of the $Z_2$
symmetry. RG equations are derived at one-loop order for both symmetric and
broken phases. The equations are consistent with those calculated in the
covariant perturbation theory. For the symmetric phase, an initial cutoff
Hamiltonian in the RG procedure is made by excluding the zero mode from the
canonical Hamiltonian with an appropriate regularization. An initial cutoff
Hamiltonian for the broken phase is constructed by shifting $\phi$ as $\phi
\rightarrow\phi-v$ in the initial Hamiltonian for the symmetric phase. The
shifted value $v$ is determined on a renormalization trajectory. The minimum of
the effective potential occurs on the trajectory.
