A field-theoretical approach to the extended Hubbard model

We transform the quartic Hubbard terms in the extended Hubbard model to a quadratic form by making the Hubbard–Stratonovich transformation for the electron operators. This transformation allows us to derive exact results for mass operator and charge–charge and spin–spin correlation functions for s-wave superconductivity. We discuss the application of the method to the d-wave superconductivity.     

Variational approach to spin fluctuations in the Hubbard model

We study a one parameter variational wave function to improve the spin density wave ground state of the Hubbard model by inclusion of quantum spin fluctuations. Using a perturbative approach and novel lattice summation techniques we present analytical as well as numerical results for the correlation energies and the staggered magnetizations in one and two dimensions. We find ground state energies which are satisfyingly close to known exact results and are significantly lower than those of existing Gutzwiller and numerical treatments.     

Asymptotically exact variational approach to the strong coupling Hubbard model

In this contribution we use a generalization of Bogoljubov's variational principle, in order to develop a molecular field theory of the Hubbard model, which becomes asymptotically exact in the strong coupling limit. For this purpose the Hamiltonian is rotated by a unitary two-particle transformation in a way which was previously introduced by Kapustin, before the variational principle is applied.Project of the Sonderforschungsbereich 65 Festkörperspektroskopie Darmstadt-Frankfurt financed by special funds of the Deutsche Forschungsgemeinschaft.     

Another approach to localized magnetic moments in the Hubbard model

By using the band part of the Hubbard Hamiltonian as our starting point, we find that for one electron/atom, with Coulomb repulsion U and bandwidth Δ, there is a single band with sharp Fermi surface and enhanced Pauli paramagnetism for U < Δ, and a splitting into two symmetric bands with local moment formation for U > Δ.     

Perturbational approach to the one particle properties of the Hubbard model

It is shown that the Hubbard model can be viewed as limiting case of a periodic Anderson model. This relation is used to set up a perturbation theory for the Hubbard model with the transfermatrixelementt as expansion parameter. One particle properties of the three dimensional Hubbard model in the half filled band case for several values of the local Coulomb interactionU calculated with this method are presented. The results give clear hints towards the formation of a gap in the excitation spectrum. The variation of the free energy on the model parameters is found to be in good agreement with expectations.This work was performed within the research program of SFB 252 Elektronisch hochkorrelierte metallische Materialien     

半满Hubbard模型的新处理方法

从标准Hubbard模型出发,对半满狭带强关联系统,在讨论自旋为δ的电子运动时,忽略自旋为-δ的电子在格点间的跳跃,得到不对称哈密顿量,并运用平均场近似求得相应准粒子谱．在绝对零度时,与Green函数近似解作了比较;在有限温度时,讨论了从绝缘体到金属相变的可能．     

多轨道Hubbard模型的隶玻色子数值算法研究

通过综合模式搜索法、广义Lagrange乘子法、以及转轴法等多种数值方法, 建立了一套针对多轨道Hubbard模型隶玻色子解法的数值优化方法. 该数值方法能够在考虑晶场劈裂、轨道间跳跃以及真实能带结构基础上, 利用隶玻色子方法计算实际关联电子材料的性质. 首先利用该方法计算了两轨道体系的Mott金属-绝缘体转变性质, 得到了与目前已有工作一致的结果; 然后利用该方法讨论了Coulomb关联对三轨道体系Na_xCoO₂的影响. 结果表明: 在中间关联情况下由e_g^'轨道形成的六个小Fermi面消失, 原因是由于电子关联导致该轨道上的空穴数随U减少. 这些结果也证实了算法的正确性和有效性. 关键词： 多轨道Hubbard模型 隶玻色子 Mott转变 xCoO₂')" href="#">Na_xCoO₂     

Spin susceptibilities for the Hubbard model in a band approach

The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω(Q)=c|Q−(π, π)| near Q∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X″(Q,ω→0) gives the same mode with a peak at Q∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X″(Q,ω→0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector. Zh. éksp. Teor. Fiz. 116, 1058–1080 (September 1999)     

Normal state properties of the attractive Hubbard model: moment approach

We introduce a two-δ-peak ansatz for the spectral density of the attractive Hubbard model in the normal state and in d-dimensions. The resulting two excitation branches and their weights are fixed in terms of the exact first four frequency moments. This ansatz correctly reproduces the atomic limit, the free case and the strong coupling limit to first order in the hopping amplitude. For this reason it is expected to provide a reasonable interpolation scheme covering the intermediate and strong coupling regimes for properties that do not depend sensitively on the damping of the two excitation branches. In the strong coupling regime, the upper excitation branch describes the creation of a fermion in an empty state, whereas the lower band arises from pair formation due to the creation of a fermion in a state already occupied by a fermion of opposite spin. Consequently, anomalous normal state properties can be expected whenever the chemical potential is within the correlation gap. This turns out to be the case when half-filling is approached for intermediate coupling as well as for any finite band filling in the strong coupling regime. In these filling and coupling regimes, there is no Fermi surface, and the formation and dissociation of pairs occur in the normal state as revealed by the temperature dependence of the double occupancy. For this reason the normal state properties exhibit an anomalous temperature dependence. Comparison with t-matrix calculations in the dilute and intermediate coupling regimes and quantum Monte Carlo estimates covering intermediate band fillings as well as intermediate and strong coupling suggest that the predictions of the moment approach are essentially correct whenever the correlation gap is not smeared out by damping effects or overlapping bands. Exploring the three-dimensional case as well, we conclude that this scenario applies to the d-dimensional attractive Hubbard model.     

Gutzwiller wave-function approach to spiral magnetic order in the two-dimensional Hubbard model: A variational Monte Carlo study

The magnetic groundstate properties of the two-dimensional Hubbard model are investigated using generalized Gutzwiller wave-functions with spiral magnetic order. Employing variational Monte Carlo simulations these wave-functions are treated without approximations on finite lattices. The resulting phase diagram shows para-, ferro-, antiferro- and spiral magnetic phases of different types.