一个扩展的Agassi模型：代数结构、phase diagram和大尺寸极限
An extended Agassi model: algebraic structure, phase diagram, and large size limit
摘要：
阿加西模型是一个示意性的两级模型，涉及配对和互作用。因此，它是著名的Lipkin-Meshkov-Glick（LMG）模型的扩展。在本文中，我们回顾了代数制定的阿加西模型的扩展，以及它的玻色子实现通过施温格表示。此外，还给出了该模型的平均场近似，并讨论了其相图。最后，利用与各能级简并度成正比的$1/j$方法，对有限个$-j$进行精确的哈密顿对角化，得到了基态能量的热力学极限和一些序参量.
英文摘要：
The Agassi model is a schematic two-level model that involves pairing and monopole-monopole interactions. It is, therefore, an extension of the well known Lipkin-Meshkov-Glick (LMG) model. In this paper we review the algebraic formulation of an extension of the Agassi model as well as its bosonic realization through the Schwinger representation. Moreover, a mean-field approximation for the model is presented and its phase diagram discussed. Finally, a $1/j$ analysis, with $j$ proportional to the degeneracy of each level, is worked out to obtain the thermodynamic limit of the ground state energy and some order parameters from the exact Hamiltonian diagonalization for finite$-j$.
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