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Journal of the Physical Society of Japan

Optical Response of Polarons and Solitons in One-Dimensional Peierls–Hubbard Model

Nobuya Maeshima, Kosuke Moriya, Ken-ichi Hino

Published Sep 30, 2012• 1 citation
Publisher

Abstract

We investigate optical properties of polarons and solitons in one-dimensional (1D) Peierls–Hubbard model by using the density matrix renormalization group method combined with the adiabatic approximation for lattice distortion. Obtained numerical results demonstrate that there appear novel midgap peaks in optical response spectra of polarons and charged-solitons for large on-site Coulomb interaction U . The origins of these novel peaks are understood in terms of charge-transfer excitations within clusters for each states: a dimer in polarons and a pentamer in charged-solitons, both of which are located around the center of the relaxed lattice distortion.

DOI
10.1143/jpsj.81.104708

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We investigate optical properties of polarons and solitons in one-dimensional (1D) Peierls–Hubbard model by using the density matrix renormalization group method combined with the adiabatic approximation for lattice distortion. Obtained numerical results demonstrate that there appear novel midgap peaks in optical response spectra of polarons and charged-solitons for large on-site Coulomb interaction U . The origins of these novel peaks are understood in terms of charge-transfer excitations within clusters for each states: a dimer in polarons and a pentamer in charged-solitons, both of which are located around the center of the relaxed lattice distortion.
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We investigate the ground state and the excitation spectrum associated with the localized defect states of the three-quarter-filled, one-dimensional Peierls-Hubbard model. In the continuum limit with an infinite, on-site electron-electron repulsion energy U, the Hamiltonian is mapped onto the N=1 Gross-Neveu model, in which irrationally charged soliton-antisoliton pairs are formed upon doping, while polarons are unstable. Corrections due to finite-U effects are discussed. However, discreteness effects are found to support excitations absent from the continuum field theory. In particular, for large band separation a novel type of polaron can be formed with a highly localized electronic wave function surrounded by an extended pattern of local lattice distortion.
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).
Density matrix renormalization group calculations of a suitably parametrized model of long polyenes (polyacetylene oligomers), which incorporate both long range Coulomb interactions and adiabatic lattice relaxation, are presented. The 13Bu+{1}^{3}{B}_{u}^{+}13Bu+​ and 21Ag+{2}^{1}{A}_{g}^{+}21Ag+​ states are found to have a 2-soliton and a 4-soliton form, respectively, both with large relaxation energies. The ${1}^{1}{B}_{u}^{\ensuremath{-}}$ 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. The soliton/antisoliton pairs are bound.
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.
As a generic model describing quasi-one-dimensional Mott and Peierls insulators, we investigate the Holstein-Hubbard model for half-filled bands using numerical techniques. Combining Lanczos diagonalization with Chebyshev moment expansion we calculate exactly the photoemission and inverse photoemission spectra, and use these to establish the phase diagram of the model. While polaronic features emerge only at strong electron-phonon couplings, pronounced phonon signatures, such as multiquanta band states, can be found in the Mott insulating regime as well. In order to corroborate the Mott to Peierls transition scenario, we determine the spin- and charge-excitation gaps by a finite-size scaling analysis based on density-matrix renormalization-group calculations.