量子集团变分法与量子铁磁$J_1$ - $J_2$模型的Phase Diagram
The Quantum Cluster Variational Method and the Phase Diagram of the quantum ferromagnetic $J_1$-$J_2$ model
摘要：
利用量子集团变分方法（QCVM）研究了量子Ising自旋的$J_1$ - $J_2$模型.我们首先描述QCVM，并讨论它是如何与其他平均场近似。在菊池近似的水平上研究了该模型的相图，在正方形晶格中作为$g = J_2/J_1$，温度和纵向和横向外部场之间的比率的函数。我们的结果表明，量子涨落可能会改变相变的顺序，并诱导铁磁相和条纹相之间的间隙。此外，当纵向场和横向场都存在时，热涨落和量子效应有助于双相的出现。
英文摘要：
We exploit the Quantum Cluster Variational Method (QCVM) to study the $J_1$-$J_2$ model for quantum Ising spins. We first describe the QCVM and discuss how it is related to other Mean Field approximations. The phase diagram of the model is studied at the level of the Kikuchi approximation in square lattices as a function of the ratio between $g = J_2/J_1$ , the temperature and the longitudinal and transverse external fields. Our results show that quantum fluctuations may change the order of the transition and induce a gap between the ferromagnetic and the stripe phases. Moreover, when both longitudinal and transverse fields are present, thermal fluctuations and quantum effects contribute to the appearance of a nematic phase.
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