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arXiv:cond-mat/9701179 · Physical review. B, Condensed matter

Structural instability in polyacene: A projector quantum Monte Carlo study

Bhargavi Srinivasan, S. Ramasesha

Published Apr 15, 1998• 20 citations
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Abstract

We have studied polyacene within the Hubbard model to explore the effect of electron correlations on the Peierls' instability in a system marginally away from one dimension. We employ the projector quantum Monte Carlo method to obtain ground-state estimates of the energy and various correlation functions. We find strong similarities between polyacene and polyacetylene which can be rationalized from the real-space valence-bond arguments of Mazumdar and Dixit. Electron correlations tend to enhance the Peierls' instability in polyacene. This enhancement appears to attain a maximum at $U/t\ensuremath{\sim}3.0$, and the maximum shifts to larger values when the alternation parameter is increased. The system shows no tendency to destroy the imposed bond-alternation pattern, as evidenced by the bond-bond correlations. The cis distortion is seen to be favored over the trans distortion. The spin-spin correlations show that undistorted polyacene is susceptible to a spin-density-wave distortion for large interaction strength. The charge-charge correlations indicate the absence of a charge-density-wave distortion for the parameters studied.

DOI
10.1103/physrevb.57.8927

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Peierls instability of a one-dimensional quantum liquid

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Whether Peierls distortion occurs for a system of one-dimensional spinless fermions is determined by the exponent g that characterizes the decay of correlations among the electrons in the undistorted state. Noninteracting electrons (g=1) is the marginal case, for which the Peierls effect just barely occurs. For repulsive interactions between the electrons (g1) the instability is enhanced and the leading dependence of the ground-state energy E on the lattice distortion \ensuremath{\delta} is E\ensuremath{\propto}-\ensuremath{\delta}${\mathrm{}}^{2/(2\mathrm{\ensuremath{-}}\mathit{g})}$. For attractive interactions (g\ensuremath{\gtrsim}1) a continuous phase transition between a normal metal and a Peierls insulator takes place for sufficiently strong electron-ion interaction. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•May 15, 1996•6 citations
We have studied polyacene within the Hubbard model to explore the effect of electron correlations on the Peierls' instability in a system marginally away from one dimension. We employ the projector quantum Monte Carlo method to obtain ground-state estimates of the energy and various correlation functions. We find strong similarities between polyacene and polyacetylene which can be rationalized from the real-space valence-bond arguments of Mazumdar and Dixit. Electron correlations tend to enhance the Peierls' instability in polyacene. This enhancement appears to attain a maximum at U/t\ensuremath∼3.0U/t\ensuremath{\sim}3.0U/t\ensuremath∼3.0, and the maximum shifts to larger values when the alternation parameter is increased. The system shows no tendency to destroy the imposed bond-alternation pattern, as evidenced by the bond-bond correlations. The cis distortion is seen to be favored over the trans distortion. The spin-spin correlations show that undistorted polyacene is susceptible to a spin-density-wave distortion for large interaction strength. The charge-charge correlations indicate the absence of a charge-density-wave distortion for the parameters studied.
We have carried out density-matrix renormalization group calculations on the ground state of long polyacene oligomers within a Pariser-Parr-Pople (PPP) Hamiltonian. The PPP model includes long-range electron correlations which are required for physically realistic modeling of conjugated polymers. We have obtained the ground-state energy as a function of the dimerization $\ensuremath{\delta}$ and various correlation functions and structure factors for $\ensuremath{\delta}=0$. From energetics, we find that the nature of the Peierls' instability in polyacene is conditional and strong electron correlations enhance the dimerization. The cis form of the distortion is favored over the trans form. However, from the analysis of correlation functions and associated structure factors, we find that polyacene is not susceptible to the formation of a bond order wave, spin-density wave, or a charge-density wave in the ground state.
On the basis of quantum Monte Carlo simulations we study the influence of "breathing" lattice distortions on the two-dimensional Hubbard model. In the half-filled band case the system remains stable against the formation of a charge-density wave already for intermediate values (U=4tU=4tU=4t) of the electronic interaction. However, the addition of holes allows for a charge-density-wave state. Thus, the structural instability is not driven by nesting of the Fermi surface, but by the combined effect of doping and Coulomb correlation. The influence of the distortion on the various pairing correlation functions is calculated.
To the conventional Peierls-Hubbard model, involving both on-site (U) and nearest-neighbor (V) Coulomb repulsions, we add ``off-diagonal'' terms, not expressible purely in terms of site densities, representing bond-bond (W) and mixed bond-site (X) electron-electron repulsive interactions involving nearest neighbors. We review earlier analyses of these interactions and discuss relative magnitudes of the parameters in applications to real materials. As a specific illustration, we investigate the effects of the off-diagonal W and X terms on dimerization in the one-dimensional, half-filled-band Peierls-Hubbard models, which have been widely applied to conjugated polymers (such as trans-polyacetylene) and to related quasi-one-dimensional charge-density wave (CDW) systems. Using both weak- and strong-coupling perturbation theory for large systems and exact diagonalizations of small systems, we investigate thoroughly the nature of the ground state of the model. For a broad range of the site-diagonal Hubbard parameters (U,V), including the values believed to be relevant to trans-polyacetylene, we find that the off-diagonal terms (W,X) initially enhance dimerization, thereby stabilizing the dimerized [or bond-order-wave (BOW)] ground state. For (unphysically) large values of W relative to U and V, dimerization is destroyed, and the BOW ground state goes over to a ferromagnetic ground state or a CDW ground state, depending on the relative sizes of U, V, and W. We conclude with a general discussion of the applicability of the Peierls-Hubbard models to quasi-one-dimensional materials, including the potential importance of the breaking of charge conjugation (``particle-hole'') symmetry by the X term.
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.
"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."
Whether Peierls distortion occurs for a system of one-dimensional spinless fermions is determined by the exponent g that characterizes the decay of correlations among the electrons in the undistorted state. Noninteracting electrons (g=1) is the marginal case, for which the Peierls effect just barely occurs. For repulsive interactions between the electrons (g1) the instability is enhanced and the leading dependence of the ground-state energy E on the lattice distortion \ensuremath{\delta} is E\ensuremath{\propto}-\ensuremath{\delta}${\mathrm{}}^{2/(2\mathrm{\ensuremath{-}}\mathit{g})}$. For attractive interactions (g\ensuremath{\gtrsim}1) a continuous phase transition between a normal metal and a Peierls insulator takes place for sufficiently strong electron-ion interaction. \textcopyright{} 1996 The American Physical Society.