Electron States of Solids Division, Faculty of Physics, Adam Mickiewicz University, Umultowska 85, PL-61-614 Poznań, Poland.
J Phys Condens Matter. 2011 Mar 16;23(10):105601. doi: 10.1088/0953-8984/23/10/105601. Epub 2011 Feb 18.
We have studied the extended Hubbard model in the atomic limit. The Hamiltonian analysed consists of the effective on-site interaction U and the intersite density-density interactions W(ij) (both nearest-neighbour and next-nearest-neighbour). The model can be considered as a simple effective model of charge ordered insulators. The phase diagrams and thermodynamic properties of this system have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case taking into account for the first time the effects of longer-ranged density-density interaction (repulsive and attractive) as well as possible phase separations shows that, depending on the values of the interaction parameters and the electron concentration, the system can exhibit not only several homogeneous charge ordered (CO) phases, but also various phase separated states (CO-CO and CO-nonordered). One finds that the model considered exhibits very interesting multicritical behaviours and features, including bicritical, tricritical, and critical end points and isolated critical points.
我们研究了原子极限下的扩展 Hubbard 模型。所分析的哈密顿量由有效局域相互作用 U 和局域密度-密度相互作用 W(ij)（包括最近邻和次近邻）组成。该模型可以被视为电荷有序绝缘体的简单有效模型。我们在变分方法的框架内确定了该系统的相图和热力学性质，该方法精确地处理局域相互作用项，而对局域相互作用项采用平均场近似。我们首次考虑了更长程密度-密度相互作用（排斥和吸引）以及可能的相分离的一般情况的研究表明，根据相互作用参数和电子浓度的不同，系统不仅可以表现出几种均匀电荷有序（CO）相，还可以表现出各种相分离状态（CO-CO 和 CO-无序）。我们发现，所考虑的模型表现出非常有趣的多临界行为和特征，包括双临界、三临界和临界点以及孤立临界点。
