Model Of Polyacetylene Research Articles

Search for kinetic properties of solitons in polyacetylenes.

The continuum model of polyacetylene is used to establish an exact evolution equation for the gap parameter accounting for both a diffusive and a double-well-originating behavior of the solitons. It is argued that this equation is a modified Korteweg--de Vries equation with opposite signs for the nonlinear and dispersive terms. As already considered by Horovitz, the sine-Gordon and ${\mathrm{cphi}}^{4}$ aspects of the soliton are shown to be complementary to one another.

Discrete symmetries and selection rules for the polyacetylene model.

The charge-conjugation and parity symmetries of the model Hamiltonian for polyacetylene as well as the selection rules implied by these symmetries for both radiative and nonradiative processes are discussed systematically. The relationship of the present discussion with previous considerations on this issue is clarified.

Existence and uniqueness of Gibbs states for a statistical mechanical polyacetylene model

One-dimensional polyacetylene is studied as a model of statistical mechanics. In a semiclassical approximation the system is equivalent to a quantumXY model interacting with unbounded classical spins in one-dimensional lattice spaceZ. By establishing uniform estimates, an infinite-volume-limit Hilbert space, a strongly continuous time evolution group of unitary operators, and an invariant vector are constructed. Moreover, it is proven that any infinite-limit state satisfies Gibbs conditions. Finally, a modification of Araki's relative entropy method is used to establish the uniqueness of Gibbs states.

A new method for simulating fermions

We apply a stochastic adaptation of the microcanonical simulation method to the numerical simulation of a non-relativistic fermionic system, the spinless Su-Schrieffer-Heeger model of polyacetylene. Various measurements expose much of the well-known physics associated with the transition to a dimerized phase and we conclude that this technique should be capable of simulating two- and three-dimensional lattice fermionic systems of interest in condensed matter physics.

Electrons and phonons in a semi-continuum model of polyacetylene

Using a modified continuum approximation to the discrete model of polyacetylene, we have obtained analytic solutions for the electronic wavefunctions in the presence of various defects which exhibit a finite band structure and reduce to exact discrete solutions in the uniformly dimerized case. This finite band model is more suitable for numerical calculation and has none of the mathematical subtleties of the fully continuum model. We have employed it to obtain an analytic expression for the phonon dispersion relation in the dimerized case, and numerical solutions for the phonon eigenfunctions on long chains in the presence of defects. We have observed a previously unidentified phenomenon: in the presence of a soliton the Goldstone mode mixes with the low lying acoustic modes, giving them a localized infrared active optic component.

The localized modes of soliton and infrared absorption in polyacetylene

Starting from SSH model of polyacetylene, anew infrared active localized mode of the soliton is found, it is the staggered mode g s, in which all the odd atoms are fixed whereas the even atoms oscillate in alternate directions. It is shown that there only exist three infrared active localized modes around the soliton, i.e. Goldstone mode, third mode and staggered mode. The effect of the electron-electron interaction on the localized modes is also studied, and the results show that all the localized modes survive e-e interaction. These three infrared active modes are well corresponding to the observed three infrared absorption lines in 900, 1288 and 1395 cm −1.

Supersymmetric treatment of random disorder in the continuum model of polyacetylene.

We employ a supersymmetric functional-integral formalism based on the method of Bohr and Efetov to study the influence of both "site" and "bond" disorder on the nature of the ground state of the continuum model of polyaceteylene. We find exact results for the electronic density of states and the amplitude of the Peierls dimerization as functions of the strength of the disorder. As the disorder is increased, the dimerization amplitude decreases to zero continuously for bond disorder and discontinuously for site disorder.

Dynamical conductivity of soliton lattice and polaron lattice in the continuum model of polyacetylene.

The dynamical conductivity due to phonons around the soliton lattice and around a polaron lattice, and the creation energy of these two structural configurations were calculated in a continuum model of polyacetylene. The crossover from the soliton lattice to the polaronlike distortion proposed by Kivelson and Heeger to explain the abrupt onset of the magnetic susceptibility around 5% doping is not found in a strictly one-dimensional calculation. The harmonic lattice fluctuations around the static equilibrium configurations were obtained and used to calculate and compare the absorption spectra for the various defect configurations.

A Polar State in a Slab as a Soluble Model of p-Wave Fermi Superfluid in Finite Geometry

A p-wave polar state whose order parameter extends perpendicular to the slab wall is analyzed in order to study the size effect in p-wave Fermi superfluids. It is shown that an order parameter profile essentialy the same as that of the half unit cell of the soliton lattice in the continuum model of polyacetylene is an analytic self-consistent solution of the gap equation. The presence of midgap states in the energy spectrum gives novel features to this model superfluid.

Solitons, polarons, and phonons in the infinite polyyne chain

The infinite polyyne chain, ( C?C ${)}_{\mathrm{\ensuremath{\infty}}}$, or polyyne, is interpreted as a Peierls distorted one-dimensional metal with strong intrinsic electron-phonon coupling at the half-filled band level. Because there are two degenerate \ensuremath{\pi}-electron bands in polyyne the effective internal degeneracy (N) of the electrons is 4, rather than 2 as in the model of polyacetylene. This leads to a rich variety of kink-soliton and polaron states and, in the limit of a continuum description, to the interesting result that polyyne is an approximate physical realization of an N=4 Gross-Neveu model relativistic field theory. The low-lying electronic excitations of the polymer are kink-solitons with charges 0, \ifmmode\pm\else\textpm\fi{}e, and \ifmmode\pm\else\textpm\fi{}2e. The lowest-lying ionization states are a polaron, a bipolaron, and a tripolaron, with charges \ifmmode\pm\else\textpm\fi{}e, \ifmmode\pm\else\textpm\fi{}2e, and \ifmmode\pm\else\textpm\fi{}3e, respectively. Photoexcitation of the polymer leads to a neutral polaron consisting of an electron and a hole bound by lattice distortion (``polarexciton''). Both the soliton and the polarons involve the appearance of localized intragap levels that are not present in the ground state. Moreover, a localized excited state exists for the polaron, while photoexcitation of the bipolaron and the tripolaron result in soliton-antisoliton pair production. Photoinduced absorption measurements on long finite polyynes in solution should be able to confirm the photogeneration of the polarexciton. Formation of the polaron states can be expected if doping with strong electron withdrawing species is possible. An ?dd?membered polyyne is predicted to contain a soliton in its ground-state configuration, the doubly ionized closed-shell chain being particularly stable. Soliton- or polaron-bearing acetylenic chains might be of relevance in astrophysics. The ground-state acoustic and optical branches of the phonon spectrum of the discrete chain are also calculated and an expression derived for the reduction of the speed of sound due to the electron-phonon coupling.

Finite-band continuum model of polyacetylene.

Many calculations involving polyacetylene use the solutions from the continuum model for the electronic eigenstates. The infinite bandwidth of this model causes difficulties. Here analytic forms for the electronic eigenstates in the presence of kinks obtained from a slightly modified continuum approximation which retains the finite-band feature of the discrete model are presented. These new solutions should provide more reliable results in all calculations.

Electronic correlations in a model of polyacetylene

The Su-Schrieffer-Heeger (SSH) model of polyacetylene is extended to include on-site and inter-site Hubbard-type electronic correlation effects. It is analysed in the continuum limit. The ground state properties are discussed within an effective single-particle (Hartree-Fock) Hamiltonian.

Lattice dynamics in the continuum model for polyacetylene

The continuum model for the coupled electron-phonon system in (CH) x is generalized by including the coupling of several relevant structural degrees of freedom to the π electron density in the model, and by including a classical lattice kinetic energy so that the lattice dynamics of the model can be studied. The model is used to study the lattice dynamics of the ideal neutral dimerized (CH) x chain and of charged with added carriers trapped at polarons and solitons. The model provides a microscopic theory explaining the appearance of a class of bound modes that are common to any mobile bond alternation defect. The full spectra of localized modes for solitons and polarons are calculated and compared. Various features in the spectra are sensitive to the topological identity and microscopic structure of the defects, and several new experimentally observable features in the spectra are analysed.

Adiabatic expansion and higher-order corrections for induced currents.

A precise expression and adiabatic expansion for the induced fermion current are given, and then some terms are calculated in a simple model of polyacetylene. A possible nonlinear term that can appear in a higher order is absent.

Non-existence of long-range order in a model of polyacetylene

Polyacetylene (CH) χ, a one-dimensional polymer, is studied as a model of quantum statistical mechanics. The effective Gibbs measure of phonons in (CH) χ is obtained by integrating out the fermion degrees of freedom, and it is shown that the effective interactions of phonons are rather complicated many-body ones but of short range (at least for small coupling constant g or for small inverse temperature β). Thus the Araki-Ruelle theory implies non-existence of long-range orders in this system.

Continuum model of a Peierls system with a complex order parameter.

We consider the continuum version of a one-dimensional model in which fermions are coupled with two phonon modes. Each mode is capable of producing dimerization, but together they are in competition, and the true ground state corresponds to only one of the two order parameters being nonzero in general. In the vicinity of a charged kink both order parameters are nonzero. We provide an analytical expression for the kink shape using the Fermi-level scheme which has been shown to be exact in another context. The gap-state energy and creation energy of the kink are also calculated. The model considered interpolates between the polyacetylene model and a model with continuous chiral symmetry in relativistic field theory.

Nonlinear Adiabatic Dynamics In Polyacetylene and Related Materials

Abstract Numerical and analytical studies of the dynamic, mean-field, adiabatic Su-Schrieffer-Heeger model of polyacetylene are shown to reveal the typical importance of strong, coherent anharmonicity, e.g. as “breathers”. Examples illustrated include (i) single kink dynamics, (ii) electron-hole (e-h) decay in trans-(CH)x; (iii) e-h decay in cis-(CH)x; (iv) e-h decay in linear polyynes; (v) decay of a photoexcited kink or polaron; (vi) photoexcitation in the presence of bond or site defects. Using a variety of examples we have shown that the adiabatic dynamics of the SSH electron-phonon model typically exhibits strongly coherent anharmonic excitations, e.g. “breathing” modes. We have emphasized situations, e.g. photoexcitation, in which the energy input is high. Breather generation with spallation neutrons should also be considered, as should thermal production in materials with narrower band gaps. Persistent, localized breathers will also be typical in the presence of “confinement” mechanisms –whether du...

Electron Localization in Polyacetylene

Abstract Electron localization in the presence of disorder and solitons in a one-dimensional tight-binding model of po-lyacetylene is analysed.

Continuum Version for the PPP Model of Polyacetylene and Other Half-Filled Peierls Systems

A continuum version is developed for the Pariser-Parr-Pople (PPP) model of polyacetylene which includes both the on-site and different site Coulomb interactions. A continuum SCF equation for π electronic and lattice structures is obtained in the approximation to take into account the terms up to O(a2) in the expansion by the lattice constant a. The SCF equation contains four gap parameters, spin dependent SCF potential and Fermi velocity which are slowly varying functions of position and depend on the Coulomb interaction. The weak coupling limit approximation which includes only the terms up to O(a) is insufficient both qualitatively and quantitatively. When the lowest correction to the weak coupling limit is taken into account, the average bond order, the effective Fermi velocity and the effective coupling constants are renormalized to have reasonable values. In this approximation, however, only the SCF solutions with one non-vanishing gap parameter are possible. Inclusion of further correction term gives the SCF solutions with coexistence of two non-vanishing gap parameters. Solitons in the PPP model are not pure amplitude solitons but amplitude-phase solitons. A soliton in the PPP model can be approximated as a phase soliton when the long range part of the Coulomb interaction is screened. The analytical expressions for neutral and charged solitons are obtained in the phase soliton approximation. The solitons connecting the SCF states with two gap parameters can have a fractional charge or a fractional spin.

Bond length alternation in cyclic polyenes. V. Local finite‐order perturbation theory approach

AbstractThe finite‐order many‐body perturbation theory using the localized Wannier orbital basis is applied to the problem of bond length alternation in the Pariser–Parr–Pople model of cyclic polyenes CN HN, N = 4v + 2, which may be regarded as a simplified model of polyacetylene. Both the Møller–Plesset and the Epstein–Nesbet‐type partitionings of the model Hamiltonian are employed. The localized orbital basis enables an efficient truncation of the perturbation theory summations over the intermediate states as well as an elimination of energetically unimportant diagrams, thus enabling one to obtain the fourth‐order Møller–Plesset‐perturbation energies with a relatively small computational effort even for large polyenes. The results obtained with the second‐, third‐, and fourth‐order Møller–Plesset and with the third‐order Epstein–Nesbet perturbation theories yield very similar bond length distortions (about 0.05 Å) and stabilization energies per site (about 0.04 eV) as obtained earlier with the RHF, one‐parameter AMO, and delocalized orbital perturbation theories. The effects of truncation and diagram elimination in the fourth‐order Møller–Plesset perturbation theory and the abnormal behavior of the second‐order Epstein–Nesbet perturbation theory results in the localized Wannier basis near the instability threshold of the RHF solutions are discussed.