  We introduce the spectrum bifurcation renormalization group (SBRG) as a
generalization of the real-space renormalization group for the many-body
localized (MBL) system without truncating the Hilbert space. Starting from a
disordered many-body Hamiltonian in the full MBL phase, the SBRG flows to the
MBL fixed-point Hamiltonian, and generates the local conserved quantities and
the matrix product state representations for all eigenstates. The method is
applicable to both spin and fermion models with arbitrary interaction strength
on any lattice in all dimensions, as long as the models are in the MBL phase.
In particular, we focus on the $1d$ interacting Majorana chain with strong
disorder, and map out its phase diagram using the entanglement entropy. The
SBRG flow also generates an entanglement holographic mapping, which duals the
MBL state to a fragmented holographic space decorated with small blackholes.
