Entanglement holographic mapping of many-body localized system by spectrum bifurcation renormalization group

We introduce the spectrum bifurcation renormalization group (SBRG) as an improved application of the excited-state real-space renormalization group (RSRG-X) for a class of qubit models. Starting from a disordered many-body Hamiltonian in the full many-body localized (MBL) phase, SBRG flows to the MBL fixed-point Hamiltonian, and generates the local integrals of motion and the matrix product state representations for all eigenstates. The method is applicable to many interacting spin and fermion models in the full MBL phase. As a Hilbert-space preserving RG, SBRG also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space.