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arXiv:cond-mat/0402184 · Physical Review B

Single-particle excitations and phonon softening in the one-dimensional spinless Holstein model

Steffen Sykora, A. Hübsch, K. W. Becker, Gerhard Wellein, Holger Fehske

Published Jan 14, 2005• 47 citations
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Abstract

We investigate the influence of the electron-phonon coupling in the one-dimensional spinless Holstein model at half-filling using both a recently developed projector-based renormalization method (PRM) and an refined exact diagonalization technique in combination with the kernel polynomial method. At finite phonon frequencies the system shows a metal-insulator transition accompanied by the appearance of a Peierls distorted state at a finite critical electron-phonon coupling. We analyze the opening of a gap in terms of the (inverse) photoemission spectral functions which are evaluated in both approaches. Moreover, the PRM approach reveals the softening of a phonon at the Brillouin-zone boundary which can be understood as precursor effect of the gap formation.

DOI
10.1103/physrevb.71.045112

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We investigate the influence of the electron-phonon coupling in the one-dimensional spinless Holstein model at half-filling using both a recently developed projector-based renormalization method (PRM) and an refined exact diagonalization technique in combination with the kernel polynomial method. At finite phonon frequencies the system shows a metal-insulator transition accompanied by the appearance of a Peierls distorted state at a finite critical electron-phonon coupling. We analyze the opening of a gap in terms of the (inverse) photoemission spectral functions which are evaluated in both approaches. Moreover, the PRM approach reveals the softening of a phonon at the Brillouin-zone boundary which can be understood as precursor effect of the gap formation.
In the spinless Holstein model at half-filling the coupling of electrons to phonons is responsible for a phase transition from a metallic state at small coupling to a Peierls distorted insulated state when the electron-phonon coupling exceeds a critical value. For the adiabatic case of small phonon frequencies, the transition is accompanied by a phonon softening at the Brillouin-zone boundary whereas a hardening of the phonon mode occurs in the anti-adiabatic case. The phonon dynamics studied in this letter do not only reveal the expected renormalization of the phonon modes but also show remarkable additional contributions due to electronic particle-hole excitations.
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.
The one-electron spectral function of the one-dimensional spin-1∕21∕21∕2 Holstein model at half filling is computed by use of the cluster perturbation theory. The cluster Green's function is obtained by the Lanczos exact diagonalization method within an optimized phonon approach. It is shown that the method allows reliable calculations using a relatively small size cluster and a few optimal phonon bases for the system from weak to strong electron-phonon coupling. In the strong-coupling limit, the spectral function shows the excitation behavior of a bipolaron state with a large gap at the Fermi surface. However, the obtained spectral function displays a metallic character in the weak-coupling regime, which is in accord with the suggestion that the Peierls gap is suppressed by quantum fluctuation of the phonons.
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.
We re-examine the Peierls insulator to Mott insulator transition scenario in the one-dimensional Holstein-Hubbard model where, at half-filling, electron-phonon and electron-electron interactions compete for establishing charge- and spin-density-wave states, respectively. By means of large-scale density-matrix renormalization group calculations we determine the spin, single-particle and two-particle excitation gaps and prove —in the course of a careful finite-size scaling analysis— recent claims for an intervening metallic phase in the weak-coupling regime. We show that for large phonon frequencies the metallic region is even more extended than previously expected, and subdivided into ordinary Luttinger-liquid and bipolaronic-liquid phases.
Summary: The interplay of charge, spin and lattice degrees of freedom is studied for quasi-one-dimensional electron and spin systems coupled to quantum phonons. Special emphasis is put on the influence of the lattice dynamics on the Peierls transition. Using exact diagonalization techniques the ground-state and spectral properties of the Holstein model of spinless fermions and of a frustrated Heisenberg model with magneto-elastic coupling are analyzed on finite chains. In the non-adiabatic regime a (T = 0) quantum phase transition from a gapless Luttinger-liquid/spin-fluid state to a gapped dimerized phase occurs at a nonzero critical value of the electron/spin-phonon interaction. To study the nature of the spin-Peierls transition at finite temperatures for the infinite system, an alternative Green’s function approach is applied to the magnetostrictive XY model. With increasing phonon frequency the structure factor shows a remarkable crossover from soft-mode to central-peak behaviour. The results are discussed in relation to recent experiments on CuGeO3. 1