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首页> 外文期刊>Annalen der Physik >Rigorous solution of a Hubbard model extended by nearest-neighbour Coulomb and exchange interaction on a triangle and tetrahedron
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Rigorous solution of a Hubbard model extended by nearest-neighbour Coulomb and exchange interaction on a triangle and tetrahedron

机译：最近邻库仑扩展的Hubbard模型的严格解以及三角形和四面体上的交换相互作用

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The Hubbard model extended by both nearest-neighbour (nn) Coulomb correlation and nearest-neighbour Heisenberg exchange is solved rigorously for a triangle and tetrahedron. All eigenvalues and eigenvectors are given as functions of the model parameters in a closed analytical form. For fixed electron numbers we found a multitude of level crossings, both in the ground state and in the excited states in dependence on the various model parameters. By coupling an ensemble of clusters to an electron bath we get the cluster gas model or the cluster gas approximation, if an extended array of weak-interacting clusters is considered. The grand-canonical potential Omega(mu, T, h) and the electron occupation N(mu, T, h) of the related cluster gases were calculated for arbitrary values (attractive and repulsive) of the three interaction constants. For the cluster gases without the additional interactions we found various steps in N(mu, T = 0, h = 0) higher than one. The reason is the degeneration of ground states differing in their electron occupation by more than one electron. For the triangular cluster gas we have one such degeneration point. For the tetrahedral cluster gas two. As a consequence, we do not find areas with one electron in the mu-U ground-state phase diagram of the triangular cluster gas or with one, two and five electrons in the case of the tetrahedral cluster gas. The degeneration point of the triangular cluster gas can not be destroyed by an applied magnetic field. This holds also for the lower degeneration point of the tetrahedral cluster gas. Otherwise, the upper degeneration point breaks down at a critical magnetic field h,. The dependence of h, on U shows a maximum for strong on-site correlation. The influence of nn-exchange and nn-Coulomb correlation on the ground-state phase diagrams is calculated. Whereas antiferromagnetic nn-exchange breaks the degeneration points of the tetrahedral cluster gas partially only, a repulsive nn-Coulomb correlation lifts the underlying degeneracies completely. Otherwise both ferromagnetic nn-exchange and attractive nn-Coulomb interaction stabilise the degeneration points. The consequences of the cluster gas results for extended cluster arrays are discussed. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.
机译：对于三角形和四面体，严格解决了由最近邻（nn）库仑相关性和最近邻海森堡交换所扩展的Hubbard模型。所有特征值和特征向量均以封闭分析形式作为模型参数的函数给出。对于固定的电子数，我们根据各种模型参数发现了在基态和激发态下的多个能级交叉。通过考虑将团簇集成到电子浴中，如果考虑了一个弱相互作用团簇的扩展阵列，则可以得到团簇气体模型或团簇气体近似值。对于三个相互作用常数的任意值（有吸引力的和排斥的），计算了相关簇气体的正典势Omega（mu，T，h）和电子占有N（mu，T，h）。对于没有其他相互作用的团簇气体，我们发现N（mu，T = 0，h = 0）高于1的各个步骤。原因是基态的退化在电子吸收方面相差一个以上的电子。对于三角形团簇气体，我们有一个这样的退化点。为四面体团簇气体两种。结果，在三角形团簇气体的mu-U基态相图中，我们找不到一个电子的区域，而在四面体团簇气体的情况下，我们找不到一个，两个和五个电子的区域。三角形团簇气体的退化点不能被施加的磁场破坏。这对于四面体团簇气体的较低变性点也成立。否则，上部退化点在临界磁场h处分解。 h对U的依赖关系显示出强烈的现场相关性最大值。计算了nn交换和nn-Coulomb相关对基态相位图的影响。反铁磁性nn交换仅部分打破了四面体簇气体的退化点，而排斥nn-Coulomb相关性则完全消除了潜在的退化。否则，铁磁nn交换和有吸引力的nn-Coulomb相互作用都会稳定变性点。讨论了簇气体结果对扩展簇阵列的影响。 （C）2008 WILEY-VCH Verlag GmbH＆Co. KGaA。温海姆。

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