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Physical Review Letters

Soliton Energetics in Peierls-Hubbard Models

David K Campbell, Thomas DeGrand, S. Mazumdar

Published May 7, 1984• 108 citations
Publisher

Abstract

We study the effect of electron-electron correlations on the energetics of solitons in electron-phonon models of quasi one-dimensional materials. In these combined Peierls-Hubbard models, by use of quantum Monte Carlo techniques, we (1) establish that the ground state of an odd chain, singly charged or neutral, is a soliton; (2) calculate neutral-soliton creation energies; and (3) prove that "soliton doping" persists in the presence of correlations. We discuss the relevance of our results for trans-polyacetylene.

DOI
10.1103/physrevlett.52.1717

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Physical review. B, Condensed matter•Jan 22, 2002•25 citations
We study the effect of electron-electron correlations on the energetics of solitons in electron-phonon models of quasi one-dimensional materials. In these combined Peierls-Hubbard models, by use of quantum Monte Carlo techniques, we (1) establish that the ground state of an odd chain, singly charged or neutral, is a soliton; (2) calculate neutral-soliton creation energies; and (3) prove that "soliton doping" persists in the presence of correlations. We discuss the relevance of our results for trans-polyacetylene.
The stationary states of a half-filled Peierls-Hubbard chain are calculated. To describe electron correlations, the wave functions as antisymmetrized products of strongly orthogonal geminals are used; wave functions and bond lengths are determined self-consistently by the variational method in an N=50 ring. The neutral soliton pair S0{S}^{0}S0S0{S}^{0}S0 is obtained as corresponding to a local total-energy minimum above the perfectly dimerized ground state. The charged soliton pair S+{S}^{+}S+${S}^{\mathrm{\ensuremath{-}}}$ refers to the minimum in the subspace of wave functions which are odd with respect to charge conjugation. The creation energies for each of the pairs are estimated as functions of Hubbard parameter U and compared with the exact excitation energies of the uniform Hubbard chain. The electron correlation is shown to make the in-gap S0{S}^{0}S0S0{S}^{0}S0 state stable even for a moderate electron-lattice coupling; the soliton width turns out to be much smaller than that in the U=0 model and comparable with the lattice constant. Applicability of the results to polyacetylene is discussed.
The one-dimensional extended Peierls-Hubbard model is studied at several band fillings using the density-matrix renormalization-group method. Results show that the ground state evolves from a Mott-Peierls insulator, with a correlation gap at half-filling, to a soliton lattice with a small band gap away from half-filling. It is also confirmed that the ground state of the Peierls-Hubbard model undergoes a transition to a metallic state at finite doping. These results show that electronic correlation effects should be taken into account in theoretical studies of doped polyacetylene. They also show that a Mott-Peierls theory could explain the insulator-metal transition observed in this material.
Using the Lanczos method for exact diagonalization on systems up to 14 sites, combined with a novel phase randomization'' technique for extracting more information from these small systems, we investigate several aspects of the one-dimensional Peierls-Hubbard Hamiltonian, in the context of trans-polyacetylene: the dependence of the ground state dimerization on the strength of the electron-electron interactions, including the effects of off-diagonal'' Coulomb terms generally ignored in the Hubbard model; the phonon vibrational frequencies and dispersion relations, and the optical absorption properties, including the spectrum of absorptions as a function of photon energy. These three different observables provide considerable insight into the effects of electron-electron interactions on the properties of real materials and thus into the nature of strongly correlated electron systems. 29 refs., 11 figs.
Effects of spin-Peierls fluctuation are examined in models of one-dimensional conductors. One-dimensional strongly correlated systems coupled to dynamical lattice distortion or polarization are examined by quantum Monte Carlo studies. Excitations are given by spinless charge solitons and neutral spin solitons when the system is doped away from a Mott insulator. A pairing mechanism due to a dynamical spin-Peierls fluctuation is discussed. Numerical results on the spin gap formation and the enhancement of pairing correlations in a dimerized t-J model and doped spin-1 Heisenberg model in one dimension are summarized.
"We have studied the extended Hubbard and the Peierls-extended Hubbard models in one dimension using primarily computational methods. We discuss the derivation of the models and the computational methods used to study them, focusing primarily on our extensions over existing numerical methods. In particular, we present the construction of ""operator-loop"" updates for spin-1/2 fermions and the inclusion of electron-phonon interactions in the Stochastic Series Expansion Quantum Monte Carlo method and the use of Quantum Parallel Tempering to improve the quality of the numerical data. For the extended Hubbard model at half-filling, we have confirmed the existence of a recently reported bond-order wave phase for the ground state in a small region of parameter space between the well-known charge- and spin-density wave phases. We have studied in detail the nature of the associated quantum phase transitions between all the phases. Upon doping away from half-filling, the doubly-degenerate, spin and charge gapped long-range-ordered ground states of the model are shown to evolve to a Luther-Emery liquid with no charge gap but a finite spin gap. For the Peierls-extended Hubbard model, which includes both electron-phonon and electron-electron interactions, we have studied the dimerization transition of the half-filled system in the presence of fully quantum mechanical phonons. We show that the transition to a dimerized state occurs only when the electron-phonon coupling exceeds a finite critical value that depends on the bare phonon frequency. This is in contrast to previous studies in similar models with adiabatic phonons that had predicted a dimerized state for arbitrarily small values of the electron-phonon coupling."
We solve a model of interacting electrons coupled to longitudinal phonons using the density matrix renormalization group method. The model is parametrized for trans-polyacetylene. We calculate the ground state and first excited odd-parity singlet and triplet states. We investigate their energies and geometries for up to 102 sites. The transition energy and the soliton width of the triplet state show significant deviations from the adiabatic approximation for chain lengths larger than the classical soliton size. In contrast, the transition energy of the singlet is close to the adiabatic prediction.