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Journal of the Physical Society of Japan

Intermediately Correlated Many-electron Systems Studied by Quantum Monte Carlo Method

Masahiro Yamazaki, Norikazu Tomita, Keiichirō Nasu

Published Mar 15, 2003• 14 citations
Publisher

Abstract

We have theoretically studied various one-dimensional half-filled Hubbard models from weak correlation cases to strong ones, and calculated the Lehmann spectra of the momentum-specified one-body Green's functions, as well as the total density of states (DOS), using the quantum Monte Carlo method. In the region of intermediate correlation strength, we have found the DOS has new characteristic peaks near the Fermi level, in addition to the well-known upper and lower Hubbard-band peaks. We show these new peaks near the Fermi level come from quasi-coherent states, while the upper and lower Hubbard-band peaks come from strongly incoherent ones. This multi-peaked structure, appearing only in the intermediate region, is shown to be quite insensitive to the dimensionality. Finally, we compare our results with the static single impurity model, and give a rough and intuitive explanation for the origin of this newly obtained multi-peaked structure. Our results also qualitatively agree with the recent experiments on CaVO 3 and SrVO 3 crystals.

DOI
10.1143/jpsj.72.611

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We have theoretically studied various one-dimensional half-filled Hubbard models from weak correlation cases to strong ones, and calculated the Lehmann spectra of the momentum-specified one-body Green's functions, as well as the total density of states (DOS), using the quantum Monte Carlo method. In the region of intermediate correlation strength, we have found the DOS has new characteristic peaks near the Fermi level, in addition to the well-known upper and lower Hubbard-band peaks. We show these new peaks near the Fermi level come from quasi-coherent states, while the upper and lower Hubbard-band peaks come from strongly incoherent ones. This multi-peaked structure, appearing only in the intermediate region, is shown to be quite insensitive to the dimensionality. Finally, we compare our results with the static single impurity model, and give a rough and intuitive explanation for the origin of this newly obtained multi-peaked structure. Our results also qualitatively agree with the recent experiments on CaVO 3 and SrVO 3 crystals.
Weights of the multimagnon (incoherent) component and the zero-magnon (coherent) one in the Lehmann's spectral representation of the one-body Green's functions are determined for the one- and the two-dimensional half-filled Hubbard models. The one-body Green's functions with specific momenta are calculated by means of a quantum Monte Carlo simulation. To distinguish the coherent component from the incoherent one in this Lehmann's spectrum, a site-diagonal staggered potential $\ensuremath{\Delta}$ is artificially added to the Hubbard models. Due to this $\ensuremath{\Delta},$ an energy gap opens in the magnon excitation, and as a result, the coherent component is clearly separated from the incoherent one. Systematic analysis on the $\ensuremath{\Delta}$ dependence of these two components shows that the weight of the coherent component is less than a few percent for each dimension in the limit of $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}0,$ which corresponds with the usual Hubbard model. This means that the incoherent component predominates the spectrum, while the coherent component makes only a minute contribution. In contrast to the widely accepted one-electron band picture, our calculations indicate that the so-called lower Hubbard band peak in the photoemission spectrum of the metal-oxide insulator originates mainly from this incoherent component. It does not correspond with the coherent one that reflects a one-electron state.
Electronic states of a two-dimensional Hubbard model near half filling is investigated by use of the composite-operator method, which is improved by including two-site correlations in combined use with the resolvent method. The densities of states obtained for the upper and lower Hubbard bands have three-peek structures at half filling and give shapes above a certain temperature similar to the ones obtained in the numerical simulation by Dagotto, Ortolani, and Scalapino [Phys. Rev. B 46, 3183 (1992)], but show narrowing of the bands at low temperature due to the formation of spin-singlet states among the nearest-neighbor electrons. A doped case shows a coherent peak at the Fermi level and the feature of the density of states is very similar to the one from numerical simulation. The one-particle spectra in the (k,k) direction is also presented. The results show that, at half filling, the spectral weight is not evenly distributed between two bands; most of the weight of the lower Hubbard band appears between (0,0) and (\ensuremath{\pi}/2a,\ensuremath{\pi}/2a), while that of the upper Hubbard band lies in the region between (\ensuremath{\pi}/2a,\ensuremath{\pi}/2a) and (\ensuremath{\pi}/a,\ensuremath{\pi}/a), keeping roughly the original band distribution. With hole doping, a flat band develops at the Fermi level with a large Fermi surface and the lower Hubbard band extends through the whole Brillouin zone.
Single-particle excitation spectra of the two-dimensional Hubbard model on the square lattice near half filling and at zero temperature are investigated on the basis of the self-consistent projection operator method. The method guarantees a high accuracy of the spectra with high energy and high momentum resolutions. It takes into account long-range intersite correlations as well as the strong on-site correlations. Effects of nonlocal excitations are clarified by comparing the results with those of the single-site approximation. The calculated spectra verify the quantum Monte-Carlo results for finite temperatures. The spectra at the Fermi level yield a hole-like Fermi surface in the underdoped region and an electron-like Fermi surface in the overdoped region. From a numerical analysis of the momentum dependent effective mass and self-energy, it is concluded that a marginal Fermi-liquid like state persists even at finite doping concentrations in the strongly correlated region because a van Hove singularity is pinned to the Fermi surface. It is also found that a kink structure appears in the quasiparticle energy band in the same region. The kink is shown to be caused by a mixing between the quasiparticle band and an excitation band with strong short-range antiferromagnetic correlations. These results suggest an explanation for some of the unusual properties of the normal state in high-TcT_{\rm c}Tc​ cuprates.
We have calculated the single-particle density of states N(\ensuremath{\omega}) and the spectral weight A(p,\ensuremath{\omega}) for the doped two-dimensional Hubbard model by combining quantum Monte Carlo simulations with the maximum-entropy analytic continuation technique. We present results for various values of the doping, temperature, and Coulomb repulsion U. For sufficiently strong Coulomb repulsions and near half filling, a Mott-Hubbard pseudogap exists. In this case, we find that a peak develops at the top of the lower Hubbard band near the Fermi level at temperatures of order of the hopping t. The structure of this peak is similar to that seen in the infinite dimensional Hubbard model.
Implementing an improved method for analytic continuation and working with imaginary-time correlation functions computed using quantum Monte Carlo simulations, we resolve the single-particle dispersion relation and the density of states (DOS) of the two-dimensional Hubbard model at half filling. At intermediate interactions of U/t=4,6U/t=4,6U/t=4,6, we find quadratic dispersion around the gap minimum at wave vectors $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ (the $\mathrm{\ensuremath{\Sigma}}$ points). We find saddle points at $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0),(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi})$ (the XXX points), where the dispersion is approximately quartic, leading to a sharp DOS maximum above the almost flat ledge arising from the states close to $\mathrm{\ensuremath{\Sigma}}$. The fraction of quasiparticle states within the ledge is ${n}_{\mathrm{ledge}}\ensuremath{\approx}0.15$. Upon doping away from half filling, within the rigid-band approximation, these results support Fermi pockets around the $\mathrm{\ensuremath{\Sigma}}$ points, with states around the XXX points becoming filled only at doping fractions $x\ensuremath{\ge}{n}_{\mathrm{ledge}}$. The high density of states away from the $\mathrm{\ensuremath{\Sigma}}$ gap edge may be an important clue for a finite minimum doping level for superconductivity and other instabilities of doped Mott insulators.
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.