Optimizing the density-matrix renormalization group method using quantum information entropy

Abstract

In order to optimize the ordering of the lattice sites in the momentum space and quantum chemistry versions of the density-matrix renormalization group (DMRG) method we have studied the separability and entanglement of the target state for the one-dimensional Hubbard model and various molecules. By analyzing the behavior of von Neumann entropy we have found criteria that help to fasten convergence. An initialization procedure has been developed which maximizes the Kullback-Leibler entropy and extends the active space in a dynamical fashion. The dynamically extended active space procedure reduces significantly the effective system size during the first half-sweep and accelerates the speed of convergence of momentum space DMRG and quantum chemistry DMRG to a great extent. The effect of lattice site ordering on the number of block states to be kept during the RG procedure is also investigated.