Symmetrized Density Matrix Renormalization Group Research Articles

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

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-hole symmetry $(J)$, and parity or spin-flip symmetry $(P)$ 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.

Low-lying excited states in armchair polyacene within Pariser-Parr-Pople model: A density matrix renormalization group study

We studied the nature of the ground state and low-lying excited states of armchair polyacene oligomers (Polyphenanthrene) within long-range Pariser-Parr-Pople model Hamiltonian with up to 14 monomers using symmetrized density matrix renormalization group technique. The ground state of all armchair polyacenes studied is found to be singlet. The results show that lowest singlet dipole allowed excited state has higher energy for armchair polyacenes as compared to linear fused polyacenes. Moreover, unlike linear fused polyacenes, the lowest singlet excited state of these oligomers is always found to lie below the lowest dipole forbidden two-photon state indicating that these armchair polyacene oligomers strongly fluoresce. The calculations of low-lying excitations on singly and triply electron doped armchair polyacene oligomers show a low energy band with strong transition dipole moment that coupled to charge conductivity. This implies armchair polyacene posses novel field-effect transistor properties.

Low-lying excitations of poly-fused thiophene within Pariser–Parr–Pople model: A density matrix renormalization group study

We studied the nature of the ground and low-lying excited states of poly-fused thiophene oligomers within long-range Pariser-Parr-Pople (PPP) model Hamiltonian with up to 14 monomers using symmetrized density matrix renormalization group technique. Our results show that the lowest dipole-allowed state lies below the lowest dipole forbidden two-photon state, indicating that poly-fused thiophenes are strongly fluorescent. The lowest triplet state lies below the two-photon state, which is in agreement with the general trend in conjugated polymers. The charge density and bond order calculations of three low-lying excited states, along with the ground state of fused thiophene oligomers, show a significant transfer of charge from sulfur to adjacent carbon atom in the middle of the largest system size and these excitations are localized. The charge density and bond order calculations on singly and doubly doped states show that bipolarons are not stable entity in these systems. The calculations of low-lying excitations on radical cation and anion of fused thiophene oligomers show a new energy band in the low energy region, which is strongly coupled to its hole and electron conductivity. This implies that poly-fused thiophenes posses novel field-effect transistor properties.

A Density Matrix Renormalization Group Study of Polyacene

We study the nature of excited states of long polyacene oligomers within a Pariser-Parr-Pople (PPP) Hamiltonian using the Symmetrized Density Matrix Renormalization Group (SDMRG) technique. We find a crossover between the two-photon state and the lowest dipole allowed excited state as the system size is increased from tetracene to pentacene. The spin-gap is the smallest gap. We also study the equilibrium geome tries in the ground and excited states from bond orders and bond-bond correlation functions. We find that the Peierls instability in the ground state of polyacene is conditional both from energetics and structure factors computed froth correlation functions.

Quantum-confinement effects on the ordering of the lowest-lying excited states in conjugated chains

The symmetrized density matrix renormalization group approach is applied within the extended Hubbard-Peierls model (with parameters U/t, V/t, and bond alternation \delta) to study the ordering of the lowest one-photon (1^{1}B^{-}_u) and two-photon (2^{1}A^{+}_g) states in one- dimensional conjugated systems with chain lengths, N, up to N=80 sites. Three different types of crossovers are studied, as a function of U/t, \delta, and N. The U-crossover emphasizes the larger ionic character of the 2A_g state compared to the lowest triplet excitation. The \delta crossover shows strong dependence on both N and U/t. The N-crossover illustrates the more localized nature of the 2A_g excitation relative to the 1B_u excitation at intermediate correlation strengths.

Symmetrized density matrix renormalization group studies of the properties of low-lying states of the poly-para-phenylene system

We report the symmetrized density matrix renormalization group (DMRG) study of neutral and doped oligomers of poly-para-phenylene (PPP) system within an extended Hubbard model. Model parameters are determined by comparing the existing results for an interacting small system. We compute a number of properties in the ground state as well as in the one-photon, two-photon and triplet states to completely characterize these states. Bond-order studies show that the lowest two-photon state corresponds to a localized excitation while one-photon and triplet excitations are extended in nature. The bipolaronic state shows clear evidence for charge separation and disproportionation into two polarons. We find that the extended nature of one-photon and triplet states of the neutral system are very similar to those of the bipolaronic ground states.

Low-lying electronic excitations and nonlinear optic properties of polymers via symmetrized density matrix renormalization group method

A symmetrized Density Matrix Renormalization Group procedure together with the correction vector approach is shown to be highly accurate for obtaining dynamic linear and third order polarizabilities of one-dimensional Hubbard and U - V models. The U - V model is seen to show characteristically different third harmonic generation response in the CDW and SDW phases. This can be rationalized from the excitation spectrum of the systems.

DMRG studies of the IB exciton binding energy and 1B/2A crossover in an extended Hubbard-Peierls model

Using a symmetrized density matrix renormalization group formulation, we have investigated the electronic binding energy (E b) of the lowest optically allowed exciton (1B) and the crossover behavior of the 1B/2A states within an extended Hubbard-Peierls model (with parameters U, V, and 5) for conjugated polymer chains with N=80. The E b value is found to be around 0.1 eV for polyacetylene and 0.22–0.45 eV for PPV when considering a realistic range of parameters. The 1B/2A crossover behavior is investigated for a wide range of parameters.