  We propose a real space renormalization group method to explicitly decouple
into independent components a many-body system that, as in the phenomenon of
spin-charge separation, exhibits separation of degrees of freedom at low
energies. Our approach produces a branching holographic description of such
systems that opens the path to the efficient simulation of the most entangled
phases of quantum matter, such as those whose ground state violates a boundary
law for entanglement entropy. As in the coarse-graining transformation of
[Phys. Rev. Lett. 99, 220405 (2007)], the key ingredient of this decoupling
transformation is the concept of entanglement renormalization, or removal of
short-range entanglement. We demonstrate the feasibility of the approach, both
analytically and numerically, by decoupling in real space the ground state of a
critical quantum spin chain into two. Generalized notions of RG flow and of
scale invariance are also put forward.
