Symmetrized density matrix renormalization group algorithm for low-lying excited states of conjugated carbon systems: Application to 1, 12-benzoperylene and …

S Prodhan, S Ramasesha - Physical Review B, 2018 - APS
Physical Review B, 2018APS
The symmetry adapted density matrix renormalization group (SDMRG) technique has been
an efficient method for studying low-lying eigenstates in one-and quasi-one-dimensional
electronic systems. However, the SDMRG method had bottlenecks involving the construction
of linearly independent symmetry adapted basis states as the symmetry matrices in the
DMRG basis were not sparse. We have developed a modified algorithm to overcome this
bottleneck. The new method incorporates end-to-end interchange symmetry (C 2), electron …
The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry , electron-hole symmetry , and parity or spin-flip symmetry in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.
American Physical Society
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