Effect of Electron-Phonon Interaction Range for a Half-Filled Band in One Dimension

Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany.
Physical Review Letters (Impact Factor: 7.51). 05/2012; 109(11). DOI: 10.1103/PhysRevLett.109.116407
Source: arXiv

ABSTRACT We demonstrate that fermion-boson models with nonlocal interactions can be
simulated at finite band filling with the continuous-time quantum Monte Carlo
method. We apply this method to explore the influence of the electron-phonon
interaction range for a half-filled band in one dimension, covering the full
range from the Holstein to the Fr\"ohlich regime. The phase diagram contains
metallic, Peierls, and phase-separated regions, which we characterize in terms
of static and dynamical correlation functions. In particular, our results
reveal a suppression of $2k_F$ charge correlations with increasing interaction
range, allowing for a power-law decay comparable to the pairing correlations.

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Available from: Fakher F. Assaad, Nov 25, 2014
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    ABSTRACT: Single-- and two-particle excitation spectra of the one-dimensional, half-filled Holstein-Hubbard model are calculated using the continuous-time quantum Monte Carlo method. In the metallic phase, the results are consistent with a Luther-Emery liquid that has gapped spin and single-particle excitations but a gapless charge mode. However, given the initially exponential dependence of the spin gap on the backscattering matrix element, the numerical excitation spectra appear gapless in the weak-coupling regime, and therefore resemble those of a Luttinger liquid. The Mott phase has the expected charge gap and gapless spin excitations. The Peierls state shows a charge, spin and single-particle gap, a soft phonon mode, backfolded shadow bands and soliton excitations. Arguments and numerical evidence for the existence of a nonzero spin gap throughout the metallic phase are provided in terms of equal-time spin and charge correlation functions.
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