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Physical review. B, Condensed matter

Effect of interactions between electrons of like spin in conducting polymers

Steven Allan Kivelson, H. B. Thacker, Weikang Wu

Published Mar 15, 1985• 21 citations
Publisher

Abstract

We consider the effects of repulsive electron-electron interactions between electrons of like spin in conducting polymers. Because the ratio W/2m of the physical bandwidth W to the band gap 2m is large in these systems, they may be represented by a field-theory model with a cutoff. When only interactions between like spins are included, the resulting model is equivalent to the massive Thirring model which has been exactly solved by Bethe's ansatz. From the exact solution we are able to conclude that perturbation theory in the interaction strength g is quite accurate so long as (g/\ensuremath{\pi})ln(W/2m)\ensuremath{\ll}1, while renormalization-group-improved perturbation theory is valid for (g/\ensuremath{\pi})\ensuremath{\ll}1. For (g/\ensuremath{\pi})\ensuremath{\gtrsim}1, results for the ground-state energy and mass gap are sensitive to the band structure far from the Fermi surface, and no simple field-theory model is adequate.

DOI
10.1103/physrevb.31.3785

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We consider the effects of repulsive electron-electron interactions between electrons of like spin in conducting polymers. Because the ratio W/2m of the physical bandwidth W to the band gap 2m is large in these systems, they may be represented by a field-theory model with a cutoff. When only interactions between like spins are included, the resulting model is equivalent to the massive Thirring model which has been exactly solved by Bethe's ansatz. From the exact solution we are able to conclude that perturbation theory in the interaction strength g is quite accurate so long as (g/\ensuremath{\pi})ln(W/2m)\ensuremath{\ll}1, while renormalization-group-improved perturbation theory is valid for (g/\ensuremath{\pi})\ensuremath{\ll}1. For (g/\ensuremath{\pi})\ensuremath{\gtrsim}1, results for the ground-state energy and mass gap are sensitive to the band structure far from the Fermi surface, and no simple field-theory model is adequate.
We present a two band fermion model consisting of a subband of conduction electrons and a subband of local electron pairs interacting via interband interactions. The model is solved in one dimension by means of the Bethe ansatz for an empty subband of local electron pairs. The ground state energy, the chemical potential, the critical exponents, describing the asymptotic behavior of correlation functions at long distances, the effective electron transport mass have been calculated numerically for an arbitrary density of conduction electrons.
We investigate the inter-play of f-electron band dispersion and inter-f electron interactions on the gap in the one electron density of states (DOS) of the periodic Anderson model. The calculations are based on dynamical mean field theory and the numerical renormalization group method for the model in infinite dimensions. The local f-electron DOS at low energies for the electron-hole symmetric model with interactions is found to have a complete-gap, a pseudo-gap or to be gap-less, whenever these structures occur for the non-interacting model but the parameters that characterize these features are strongly renormalized. As the degree of f-electron dispersion is increased, when there is a complete gap, the many-body renormalization remains almost constant, but in the pseudo-gap case the renormalization increases. We calculate the sizes of gaps both in the local DOS and in the dynamic local susceptibilities. When the gap width is defined by the edges in the spectrum for the complete-gap model, the widths of the indirect gap and the spin gap are equal, independent of the degree of electron correlation. However, if the width is defined as the excitation energy between the peaks in the spectrum, then the ratio of the indirect gap to the spin gap increases and eventually saturates as the correlation increases. The value of this ratio depends on the f-electron band dispersion. We have also investigated the dependence of the shape of the interacting DOS on the f-band filling for different forms of f-band dispersion. When the f-band dispersion is small, the gap structure in the symmetric model vanishes as the filling factor decreases. When the model, including the dispersion, has no gap structure, the filling dependence on the DOS in low energies is similar to that for a single impurity Anderson model. The energy dispersion of the quasi-particle in the range, ε f < ε < ε f + U , is approximately explained by the renormalized band model in the cases of both large and small f-band dispersion.
A model of interacting electrons living on two chains coupled by a transverse hopping ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ is solved exactly by a bosonization technique. It is shown that ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ does modify the shape of the Fermi surface also in the presence of interaction, although charge and spin excitations keep different velocities ${\mathit{u}}_{\mathrm{\ensuremath{\rho}}}$, ${\mathit{u}}_{\mathrm{\ensuremath{\sigma}}}$. Two different regimes occur: At short distances, x\ensuremath{\ll}\ensuremath{\xi}=(${\mathit{u}}_{\mathrm{\ensuremath{\rho}}}$-${\mathit{u}}_{\mathrm{\ensuremath{\sigma}}}$)/4${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$, the two chain model is not sensitive to ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$, while for larger separation x\ensuremath{\gg}\ensuremath{\xi} interchain hopping is relevant and generates further singularities in the electron Green function besides those due to spin-charge decoupling.
The accurate analytical and numerical calculations of the electronic band structure and ground state properties of strongly correlated electrons within the Hubbard model are performed by constructing convergent perturbation theory for general interaction strength and electron concentration. We test the developed perturbation approach about mean field solution in the extreme conditions of one dimensionality for entire parameter space of electron interaction U/t and electron concentration n. The many-body perturbation formalism up two second order about the generalized self-consistent field (GSCF) Hamiltonian goes beyond the range of applicability of standard perturbation theory by incorporating systematically the effect of the random-phase-type perturbation techniques and controlled expansion of the energy functional for general U/t and n. The second order perturbation correction vanishes at small and large U/t limit and performed calculations of the ground state energy show a next to the perfect numerical agreement with the Bethe-ansatz results.
[[abstract]]The accurate analytical and numerical calculations of the electronic band structure and ground state properties of strongly correlated electrons within the Hubbard model are performed by constructing convergent perturbation theory for general interaction strength and electron concentration. We test the developed perturbation approach about mean field solution in the extreme conditions of one dimensionality for entire parameter space of electron interaction U/t and electron concentration n. The many-body perturbation formalism up two second order about the generalized self-consistent field (GSCF) Hamiltonian goes beyond the range of applicability of standard perturbation theory by incorporating systematically the effect of the random-phase-type perturbation techniques and controlled expansion of the energy functional for general U/t and n. The second order perturbation correction vanishes at small and large U/t limit and performed calculations of the ground state energy show a next to the perfect numerical agreement with the Bethe-ansatz results.
Based on a positive semidefinite operator technique, exact ground states are deduced for the non-integrable conducting polymers possessing pentagon type of unit cell. The study is done in the presence of many-body spin-orbit interaction (SOI), local and nearest neighbor Coulomb repulsion (NNCR) and presence of external EEE electric and BBB magnetic fields, such that the effects of BBB on both orbital and spin degrees of freedom is considered. The SOI, NNCR, and presented external field configurations presence in exact conducting polymer ground states is a novelty, so the development of the technique for the treatment possibility of such strongly correlated cases is presented in details. The deduced ground states show a broad spectrum of physical characteristics ranging from charge density waves, metal-insulator transitions, to interesting external field driven effects as e.g. modification possibility of a static charge distribution by a static external magnetic field.