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Physical review. B, Condensed matter

Dynamical nonlinear optical coefficients from the symmetrized density-matrix renormalization-group method

Swapan Kumar Pati, S. Ramasesha, Zhigang Shuai, Jean‐Luc Brédas

Published Jun 15, 1999• 53 citations
Publisher

Abstract

We extend the symmetrized density-matrix renormalization-group method to compute the dynamic nonlinear optical coefficients for long chains. By computing correction vectors in the appropriate symmetry subspace, we obtain the dynamic polarizabilities, ${\ensuremath{\alpha}}_{\mathrm{ij}}(\ensuremath{\omega})$, and third-order polarizabilities ${\ensuremath{\gamma}}_{\mathrm{ijkl}}(\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})$ of the Hubbard and ``U-V'' chains in an all transpolyacetylene geometry, with and without dimerization. We rationalize the behavior of $\overline{\ensuremath{\alpha}}$ and $\overline{\ensuremath{\gamma}}$ on the basis of the low-lying excitation gaps in the system.

DOI
10.1103/physrevb.59.14827

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We extend the symmetrized density-matrix renormalization-group method to compute the dynamic nonlinear optical coefficients for long chains. By computing correction vectors in the appropriate symmetry subspace, we obtain the dynamic polarizabilities, \ensuremathαij(\ensuremathω){\ensuremath{\alpha}}_{\mathrm{ij}}(\ensuremath{\omega})\ensuremathαij​(\ensuremathω), and third-order polarizabilities \ensuremathγijkl(\ensuremathω,\ensuremathω,\ensuremathω){\ensuremath{\gamma}}_{\mathrm{ijkl}}(\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})\ensuremathγijkl​(\ensuremathω,\ensuremathω,\ensuremathω) of the Hubbard and ``U-V'' chains in an all transpolyacetylene geometry, with and without dimerization. We rationalize the behavior of \ensuremathα‾\overline{\ensuremath{\alpha}}\ensuremathα​ and \ensuremathγ‾\overline{\ensuremath{\gamma}}\ensuremathγ​ on the basis of the low-lying excitation gaps in the system.
We extend the symmetrized density matrix renormalization group (SDMRG) method to compute the dynamic nonlinear optic coefficients for long chains. By computing correction vectors in the appropriate symmetry subspace we obtain the dynamic polarizabilities, αij(ω)α_{ij}(ω)αij​(ω), and third-order polarizabilities γijkl(ω,ω,ω)γ_{ijkl}(ω,ω,ω)γijkl​(ω,ω,ω) of the Hubbard and "U−VU-VU−V" chains in an all−transall-transall−trans polyacetylene geometry, with and without dimerization. We rationalize the behavior of αˉ\barααˉ and γˉ\barγγˉ​ on the basis of the low-lying excitation gaps in the system. This is the first study of the dynamics of a fermionic system within the DMRG framework.
We extend the density-matrix renormalization-group (DMRG) method to exploit parity, C2{\mathit{C}}_{2}C2​ (rotation by \ensuremath{\pi}), and electron-hole symmetries of model Hamiltonians. We demonstrate the power of this method by obtaining the lowest-energy states in all eight symmetry subspaces of Hubbard chains with up to 50 sites. The ground-state energy, optical gap, and spin gap of regular U=4t and U=6t Hubbard chains agree very well with exact results. This development extends the scope of the DMRG method and allows future applications to study of optical properties of low-dimensional conjugated polymeric systems. \textcopyright{} 1996 The American Physical Society.
We extend the density matrix renormalization group method to exploit Parity, C2C_2C2​ (rotation by πππ) and electron-hole symmtries of model Hamiltonians. We demonstrate the power of this method by obtaining the lowest energy states in all the eight symmetry subspaces of Hubbard chains with upto 50 sites. The ground-state energy, optical gap and spin gap of regular U=4tU=4tU=4t and U=6tU=6tU=6t Hubbard chains agree very well with exact results. This development extends the scope of the DMRG method and allows future applications to study of optical properties of low-dimensional conjugated polymeric systems.
The density-matrix renormalization group (DMRG) method is used for a comparative study of low-lying excitations in trans-polyacetylene (t-PA) and transversely substituted t-PA (TS-t-PA). We have employed the Pariser-Parr-Pople model Hamiltonian which incorporates long-range electronic correlations to model these systems. We find some fundamental differences in the excited states of the t-PA and TS-t-PA. We find that the lowest two-photon allowed excited state in TS-t-PA is not made up of two triplet excitons and the gap to this state is nonzero even for undimerized chains in the thermodynamic limit. Contrary to earlier results for the Hubbard model, we find that the lowest two-photon state is always below the first optically allowed state in all the systems studied here making TS-t-PA systems only weakly fluorescent materials. Nonresonant tumbling averaged linear and third harmonic generation optic coefficients of TS-t-PA systems are also much smaller than that of t-PA.
We report accurate numerical studies of excited state orderings in long hypothetical $\ensuremath{\pi}$-conjugated oligomers in which the hydrogen atoms of transpolyacetylene are replaced with conjugated side groups, within modified Hubbard models. There exists a range of the bare Coulomb repulsion for which the excited state ordering is conducive to photoluminescence in the substituted systems, even as this ordering is opposite in the unsubstituted polyenes of the same lengths. Our work provides motivation to study real $\ensuremath{\pi}$-conjugated polymers with transverse conjugation and small optical gaps.