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近代物理研究所和兰州重离子加速器实验室年报：英文版

Equation of Motion Approach to Two—dimensional Hubbard Model

Luo, HGWang, Sjspectral Weight

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

Using a Green's-function equation of motion approach the two-dimensional Hubbard model is studied. The decoupling of the hierarchy is performed according to the conserving of the first four spectral moments. Beyond the Roth's two-pole approximation, the damping effect occurs naturally. The energy dispersions at various fillings, the spectral weight, and the density of states are calculated. Comparisons with the quantum Monte Carlo results and the cluster perturbation theory show that our approach can capture some essential features of the Hubbard model.

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Using a Green's-function equation of motion approach the two-dimensional Hubbard model is studied. The decoupling of the hierarchy is performed according to the conserving of the first four spectral moments. Beyond the Roth's two-pole approximation, the damping effect occurs naturally. The energy dispersions at various fillings, the spectral weight, and the density of states are calculated. Comparisons with the quantum Monte Carlo results and the cluster perturbation theory show that our approach can capture some essential features of the Hubbard model.
Using a Green's-function equation of motion approach the two-dimensional Hubbard model is studied. The decoupling of the hierarchy is performed according to the conserving of the first four spectral moments. Beyond the Roth's two-pole approximation, the damping effect occurs naturally. The energy dispersions at various fillings, the spectral weight, and the density of states are calculated. Comparisons with the quantum Monte Carlo results and the cluster perturbation theory show that our approach can capture some essential features of the Hubbard model.
We study the spectral function of the two-dimensional Hubbard model using cluster perturbation theory, and a density matrix renormalization group as a cluster solver. We reconstruct the two-dimensional dispersion at and away from half-filling using $2\ifmmode\times\else\texttimes\fi{}L$ ladders, with LLL up to 80 sites, yielding results with unprecedented resolution in excellent agreement with quantum Monte Carlo. The main features of the spectrum can be described with a mean-field dispersion, with kinks and pseudogap traced back to scattering between spin and charge degrees of freedom.
A well-established method to deal with highly correlated systems is based on the expansion of the Green's function in terms of spectral moments. In the context of the Composite Operator Method one approximation is proposed: a set of n composite fields is assumed as fundamental basis and the dynamics is considered up to the order s. The resulting Green's function has a sn-pole structure. The truncation of the hierarchy of the equations of motion is made at the s-th order and the first s-1 equations are treated exactly. A theorem, which rules the conservation of the spectral moments, is presented. The procedure is applied to the Hubbard model and a recurrence relation for the calculation of its electronic spectral moments is derived.
The two-dimensional Hubbard model is analyzed in the framework of the two-pole expansion. It is demonstrated that several theoretical approaches, when considered at their lowest level, are all equivalent and share the property of satisfying the conservation of the first four spectral momenta. It emerges that the various methods differ only in the way of fixing the internal parameters and that it exists a unique way to preserve simultaneously the Pauli principle and the particle–hole symmetry. A comprehensive comparison with respect to some general symmetry properties and the data from quantum Monte Carlo analysis shows the relevance of imposing the Pauli principle.
Abstract Equations for the electron Green's function of the two‐dimensional Hubbard model, derived using the strong coupling diagram technique, are self‐consistently solved for different electron concentrations n and tight‐binding dispersions. Comparison of spectral functions calculated for the ratio of Hubbard repulsion to the nearest neighbor hopping with Monte Carlo data shows not only qualitative, but in some cases quantitative agreement in position of maxima. General spectral shapes, their evolution with momentum and filling in the wide range are also similar. At half‐filling and for the next nearest neighbor hopping constant the Mott transition occurs at , where is the initial bandwidth. This value is close to those obtained in the cases of the semi‐elliptical density of states and for . In the case and the Mott gap reaches maximum width at , and it is larger than that at for half‐filling. In all considered cases positions of spectral maxima are close to those in the Hubbard‐I approximation.
We present results for the single-particle spectral weight function for the two-dimensional Hubbard model. Results were obtained using analytic expressions for the first two moments of the spectral weight function, along with numerical calculations using a combination of quantum Monte Carlo and the maximum-entropy method of analytic continuation. The expressions for the first two moments are surprisingly simple, involving only the parameters of the model, the chemical potential, and the filling. At half-filling, the squared width (variance) of the spectral weight is exactly U2{\mathit{U}}^{2}U2/4. Numerical results are shown for 8\ifmmode\times\else\texttimes\fi{}8 lattices at a variety of fillings and momenta. The insulating antiferromagnetic gap in the spectral weights, readily apparent in the results at half-filling, is absent at a filling of 0.95.