Density matrix renormalization group development

The Hubbard model, which has played a significant part in the earlier development of nonlinear optical response theory of molecules, has been revived by Shehadi et al.203 to explain the properties of small bridged metallic polymers. The Hubbard-Peierls hamiltonian has also been used by Shuai et al.,204 in conjunction with a symmetry adapted density matrix renormalization group formulation, to calculate a number of properties, including third harmonic generation in trans-octatetraene. 

Recently, the key problems associated with the failure of the old RG method have been identified and a different renormalization procedure based on the eigenvalues of the many-body density matrix of proper subsystems has been developed [64, 65]. This method has come to be known as the density matrix renormalization group (DMRG) method and has found dramatic success in dealing with... 

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