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Molecular Physics

Rigorous treatment of strong electronic correlations in polydiacetylene chains

Gergely Barcza, Florian Gebhard, Örs Legeza

Published Jun 21, 2013• 5 citations
Publisher

Abstract

We study theoretically polydiacetylene chains diluted in their monomer matrix. We employ the density-matrix renormalisation group method (DMRG) on finite chains to calculate the ground state and low-lying excitations of the corresponding Peierls–Hubbard-Ohno Hamiltonian that is characterised by the electron transfer amplitude t 0 between nearest-neighbours, by electron–phonon coupling constant α, by Hubbard interaction U, and by long-range interaction V. We treat lattice relaxation in the adiabatic limit, i.e., we calculate the polaronic lattice distortions for each excited state. We present accurate DMRG results for the single-particle gap, the singlet exciton, the triplet ground state and its optical excitation, and find a good agreement with experimental data for PDA–3BCMU chains. Using a fairly stiff spring constant, the length of our unit cell is about 1% larger than observed in experiment.

DOI
10.1080/00268976.2013.809164

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We study theoretically polydiacetylene chains diluted in their monomer matrix. We employ the density-matrix renormalisation group method (DMRG) on finite chains to calculate the ground state and low-lying excitations of the corresponding Peierls–Hubbard-Ohno Hamiltonian that is characterised by the electron transfer amplitude t 0 between nearest-neighbours, by electron–phonon coupling constant α, by Hubbard interaction U, and by long-range interaction V. We treat lattice relaxation in the adiabatic limit, i.e., we calculate the polaronic lattice distortions for each excited state. We present accurate DMRG results for the single-particle gap, the singlet exciton, the triplet ground state and its optical excitation, and find a good agreement with experimental data for PDA–3BCMU chains. Using a fairly stiff spring constant, the length of our unit cell is about 1% larger than observed in experiment.
We study theoretically polydiacetylene chains diluted in their monomer matrix. We employ the density matrix renormalization group method on finite chains to calculate the ground state and low-lying excitations of the corresponding Peierls--Hubbard-Ohno Hamiltonian which is characterized by the electron transfer amplitude t0{t}_{0}t0​ between nearest neighbors, by the electron-phonon coupling constant $\ensuremath{\alpha}$, by the Hubbard interaction UUU, and by the long-range interaction VVV. We treat the lattice relaxation in the adiabatic limit, i.e., we calculate the polaronic lattice distortions for each excited state. Using chains with up to 102 lattice sites, we can safely perform the extrapolation to the thermodynamic limit for the ground-state energy and conformation, the single-particle gap, and the energies of the singlet exciton, the triplet ground state, and the optical excitation of the triplet ground state. The corresponding gaps are known with high precision from experiments. We determine a coherent parameter set $({t}_{0}^{*}=2.4\phantom{\rule{0.16em}{0ex}}\mathrm{eV},{\ensuremath{\alpha}}^{*}=3.4\phantom{\rule{0.16em}{0ex}}\mathrm{eV}/\text{\AA{}},{U}^{*}=6\phantom{\rule{0.16em}{0ex}}\mathrm{eV},{V}^{*}=3\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$ from a fit of the experimental gap energies to the theoretical values which we obtain for 81 parameter points in the four-dimensional search space $({t}_{0},\ensuremath{\alpha},U,V)$. We identify dark in-gap states in the singlet and triplet sectors as seen in experiments. Using a fairly stiff spring constant, the length of our unit cell is about 1% larger than its experimental value.
We study the elementary excitations of a model Hamiltonian for the $\ensuremath{\pi}$ electrons in polydiacetylene chains. In these materials, the bare band gap is only half the size of the observed single-particle gap and the binding energy of the exciton of 0.5 eV amounts to 20% of the single-particle gap. Therefore, exchange and correlations due to the long-range Coulomb interaction require a numerically exact treatment which we carry out using the density-matrix renormalization group method. Employing both the Hubbard-Ohno potential and the screened potential in one dimension, we reproduce the experimental results for the binding energy of the singlet exciton and its polarizability. Our results indicate that there are optically dark states below the singlet exciton, in agreement with experiment. In addition, we find a weakly bound second exciton with a binding energy of 0.1 eV. The energies in the triplet sector do not match the experimental data quantitatively, probably because we do not include polaronic relaxation effects.
We present density-matrix renormalization-group calculations of the Pariser-Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (13Bu+)(1{}^{3}{B}_{u}^{+})(13Bu+​) and even-parity singlet (21Ag+)(2{}^{1}{A}_{g}^{+})(21Ag+​) states have a 2-soliton and 4-soliton forms, respectively, both with large relaxation energies. The dipole-allowed $(1{}^{1}{B}_{u}^{\ensuremath{-}})$ state forms an exciton-polaron, and has a very small relaxation energy. The relaxed energy of the 21Ag+2{}^{1}{A}_{g}^{+}21Ag+​ state lies below that of the $1{}^{1}{B}_{u}^{\ensuremath{-}}$ state. We observe an attraction between the soliton-antisoliton pairs in the 21Ag+2{}^{1}{A}_{g}^{+}21Ag+​ state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepancies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. Electronic interactions play the key role in determining the ground-state dimerization and the excited-state transition energies.
In this work the optical excitations in the one-dimensional extended Peierls-Hubbard model are studied. There are two competing interactions in this model, namely the Coulomb interaction and the Peierls interaction. The latter causes a dimerised lattice structure. To calculate the optical excitations perturbatively, one needs to identify the dominant interaction of the model. In the field-theoretical limit using different methods, such as a semiclassical approach, mean-field theory and the renormalisation group, one finds that it is the Peierls-interaction which dominates the system and therefore defines the starting point for perturbation theory. Rayleigh-Schrödinger perturbation theory is carried out up to second order in the weak Coulomb interaction for the ground-state energy and the one-particle gap. The singlet and triplet exciton gaps, i.e. charge and spin gap, are calculated using Wannier perturbation theory, two-step perturbation theory and Downfolding perturbation theory. All results are compared to results obtained by using the density-matrix renormalisation group approach (DMRG).
We have applied a numerical renormalization-group technique to study the Hubbard-Peierls model for (CH)x{)}_{\mathrm{x}})x​. The method provides accurate many-body wave functions and energies for the ground and low-lying excited states of finite polyenes. We report tests of the method for finite chains (N=16) which show that the technique accurately reproduces known results in the noninteracting particle limit (U=0) and in the highly correlated limit (U/4t\ensuremath{\gg}1) and agrees well with Monte Carlo data where available for intermediate U. The model is applied to study correlation effects on the ground-state dimerization amplitude and to the ordering of the low-lying excited states of the rigid-lattice spectrum. Extension of the method to even longer systems appears to be quite practical.
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.