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arXiv:cond-mat/9803245 · Physical review. B, Condensed matter

Peierls instability and optical response in the one-dimensional half-filled Holstein model of spinless fermions

Alexander Weiße, Holger Fehske

Published Nov 15, 1998• 50 citations
arXivHTMLPDF

Abstract

The effects of quantum lattice fluctuations on the Peierls transition are studied within the one-dimensional Holstein molecular-crystal model by means of exact diagonalization methods. Applying a very efficient variational Lanczos technique, the ground-state phase diagram is obtained in excellent agreement with predictions of recent density matrix renormalization-group calculations. The transition to the charge-density-wave regime is signaled by a strong increase in the charge structure factor. In the metallic regime, the nonuniversal Luttinger liquid parameters (charge velocity and coupling constant) are deduced from a finite-size scaling analysis. The variational results are supported by a complete numerical solution of the quantum phonon Holstein model on small clusters, which is based on a well-controlled phonon Hilbert space truncation procedure. The metallic and charge-density-wave phases are characterized by significant differences in the calculated optical-absorption spectra.

DOI
10.1103/physrevb.58.13526

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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.
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The Holstein model of spinless fermions interacting with dispersionless phonons in one dimension is studied by a Green's function Monte Carlo technique. The ground-state energy, first fermionic excited state, density wave correlations, and mean lattice displacements are calculated for lattices of up to 16 sites, for one fermion per two sites, i.e., a half-filled band. Results are obtained for values of the fermion hopping parameter of t=0.1\ensuremath{\omega}, \ensuremath{\omega}, and 10\ensuremath{\omega}, where \ensuremath{\omega} is the phonon frequency. At a finite fermion-phonon coupling g there is a transition from a metallic phase to an insulating phase in which there is charge-density-wave order. Finite-size scaling is found to hold in the metallic phase and is used to extract the coupling dependence of the Luttinger liquid parameters, ${\mathit{u}}_{\mathrm{\ensuremath{\rho}}}$ and ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$, the velocity of charge excitations, and the correlation exponent, respectively. For free fermions (g=0) and for strong coupling (g2{\mathit{g}}^{2}g2\ensuremath{\gg}t\ensuremath{\omega}) our results agree well with known analytic results. \textcopyright{} 1996 The American Physical Society.
Electron- and phonon spectral functions of the one-dimensional, spinless-fermion Holstein model at half filling are calculated in the four distinct regimes of the phase diagram, corresponding to an attractive or repulsive Luttinger liquid at weak electron-phonon coupling, and a band- or polaronic insulator at strong coupling. The results obtained by means of kernel polynomial and systematic cluster approaches reveal substantially different physics in these regimes and further indicate that the size of the phonon frequency significantly affects the nature of the quantum Peierls phase transition, the latter being either of the soft-mode or central-peak type. The generic features observed are relevant to several classes of low-dimensional materials.
The effects of quantum lattice fluctuations on the Peierls transition and the optical conductivity in the one-dimensional Holstein model of spinless fermions have been studied by developing an analytical approach based on the unitary transformation method. We show that when the electron-phonon coupling constant decreases to a finite critical value, the Peierls dimerization is destroyed by the quantum lattice fluctuations. The dimerization gap is much more reduced by the quantum lattice fluctuations than the phonon order parameter. The calculated optical conductivity does not have the inverse-square-root singularity, but it has a peak above the gap edge, and there exists a significant tail below the peak. The peak of optical-conductivity spectrum is not directly corresponding to the dimerized gap. Our results of the phase diagram and the spectral-weight function agree with those of the density-matrix renormalization group and the exact diagonalization methods.
We study the one-dimensional Holstein model with spin-12\frac{1}{2}21​ electrons at half filling. Ground-state properties are calculated for long chains with great accuracy using the density-matrix renormalization-group method and extrapolated to the thermodynamic limit. We show that for small electron-phonon coupling or large phonon frequency, the insulating Peierls ground state predicted by mean-field theory is destroyed by quantum lattice fluctuations and that the system remains in a metallic phase with a nondegenerate ground state and power-law electronic and phononic correlations. When the electron-phonon coupling becomes large or the phonon frequency small, the system undergoes a transition to an insulating Peierls phase with a twofold degenerate ground state, long-range charge-density-wave order, a dimerized lattice structure, and a gap in the electronic excitation spectrum.