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arXiv:cond-mat/0606748 · Physical Review B

Spin and charge dynamics of the one-dimensional extended Hubbard model

H. Benthien, Eric Jeckelmann

Published May 29, 2007• 47 citations
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Abstract

We investigate the dynamical spin and charge structure factors and the one-particle spectral function of the one-dimensional extended Hubbard model at half band filling using the dynamical density-matrix renormalization-group method. The influence of the model parameters on these frequency- and momentum-resolved dynamical correlation functions is discussed in detail for the Mott-insulating regime. We find quantitative agreement between our numerical results and experiments for the optical conductivity, resonant inelastic x-ray scattering, neutron scattering, and angle-resolved photoemission spectroscopy in the quasi-one-dimensional Mott insulator $\mathrm{Sr}\mathrm{Cu}{\mathrm{O}}_{2}$.

DOI
10.1103/physrevb.75.205128

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We investigate the dynamical spin and charge structure factors and the one-particle spectral function of the one-dimensional extended Hubbard model at half band filling using the dynamical density-matrix renormalization-group method. The influence of the model parameters on these frequency- and momentum-resolved dynamical correlation functions is discussed in detail for the Mott-insulating regime. We find quantitative agreement between our numerical results and experiments for the optical conductivity, resonant inelastic x-ray scattering, neutron scattering, and angle-resolved photoemission spectroscopy in the quasi-one-dimensional Mott insulator SrCuO2\mathrm{Sr}\mathrm{Cu}{\mathrm{O}}_{2}SrCuO2​.
Recent angle-resolved photoemission spectroscopy (ARPES) for a newly discovered doped one-dimensional (1D) Mott insulator ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ proposed the presence of attractive charge interactions between neighboring sites if a 1D Hubbard model is employed to describe the material. On the other hand, long-range repulsive charge interactions were proposed to be crucial for understanding the optical excitations of undoped 1D Mott insulators. Motivated by these contrasting proposals, we perform density-matrix renormalization group calculations of the single-particle spectral function as well as dynamical spin and charge structure factors for two kinds of extended 1D Hubbard models. The spectral function for the long-range repulsive model less agrees with the ARPES data as compared with that for the attractive one. The dynamical spin and charge structure factors also exhibit contrasting behaviors between the two models: The attractive model shows less momentum dependence of the integrated weight in the dynamical spin structure factor and more accumulation of the weight on the upper edge of particle-hole-type excitation in the dynamical charge structure factor. These features give a good criterion of an appropriate model for doped 1D Mott insulators, which can be judged by resonant-inelastic x-ray scattering experiments.
We examine the single-particle excitation spectrum in the one-dimensional Hubbard-Holstein model at half-filling by performing a dynamical density matrix renormalization group calculation. The spin-charge separation is robust against the electron-phonon (EP) coupling, although both spinon and holon branches are affected by phonons. We find that this robustness is in sharp contrast to a rather strong influence of the EP coupling on quasiparticle properties in two dimensions. We discuss the implication of the results of recent angle-resolved photoemission spectroscopy measurements on SrCuO2\mathrm{Sr}\mathrm{Cu}{\mathrm{O}}_{2}SrCuO2​.
We calculate the photoemission spectral function of the one-dimensional Hubbard model away from half filling using the dynamical density-matrix renormalization group method. An approach for calculating momentum-dependent quantities in finite open chains is presented. Comparison with exact Bethe ansatz results demonstrates the unprecedented accuracy of our method. Our results show that the photoemission spectrum of the quasi-one-dimensional conductor TTF-TCNQ provides evidence for spin-charge separation on the scale of the conduction bandwidth.
Abstract We numerically investigate spectroscopic properties for a two-dimensional Mott insulator described by a half-filled Hubbard model on the square lattice. Firstly, we examine the spectral shape of the optical conductivity by using time-dependent density-matrix renormalization group implemented by the Legendre polynomial expansion. We find a shape peak resembling to an excitonic peak at absorption edge, whose origin is attributable to antiferromagnetic correlation in the spin background. We next investigate momentum-dependent transient charge and spin dynamics after photoirradiation by using time-dependent Lanczos-type exact diagonalization. We find a temporal oscillation in the intensity of the dynamical spin structure factor, which exhibits an antiphase behavior between, for example, two orthogonal momentum directions parallel and perpendicular to the electric field of a pump pulse. Observing such antiphase oscillations will be a big challenge for time-resolved resonant-inelastic x-ray scattering experiments.
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.
Quasi-one-dimensional (1D) materials provide a unique platform for understanding the importance and influence of extended interactions on the physics of strongly correlated systems due to their relative structural simplicity and the existence of powerful theoretical tools well adapted to one spatial dimension. Recently, this was highlighted by anomalous observations in the single-particle spectral function $A(q,\ensuremath{\omega})$ of 1D cuprate chain compounds, measured by angle-resolved photoemission spectroscopy (ARPES), which were explained by the presence of a long-range attractive interaction. Such an extended interaction should leave its fingerprints on other observables, notably the dynamical spin structure factor $S(q,\ensuremath{\omega})$, measured by neutron scattering or resonant inelastic x-ray scattering. Starting from a simple Hubbard Hamiltonian in 1D and using time-dependent density matrix renormalization group methods, we show that the presence of long-range attractive coupling, directly through an instantaneous Coulomb interaction VVV or retarded electron-phonon (el-ph) coupling, can introduce significant spectral weight redistribution in $S(q,\ensuremath{\omega})$ across a wide range of doping. This underscores the significant impact that extended interactions can have on dynamical correlations among particles, and the importance of properly incorporating this influence in modeling. Our results demonstrate that $S(q,\ensuremath{\omega})$ can provide a sensitive experimental constraint, which complements ARPES measurements, in identifying key interactions in 1D cuprates, beyond the standard Hubbard model.