The coupled cluster method applied to quantum magnetism
The coupled cluster method applied to quantum magnetism
复制标题
耦合簇法在量子磁学中的应用
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Raymond F. Bishop
中科院分区：
文献类型：
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作者：
D. Farnell;Raymond F. Bishop
耦合簇方法（CCM）是量子多体理论中最强大、应用最广泛的技术之一。特别地，它被广泛地用于研究许多类型的晶格量子自旋系统在零温度下。这些系统的基态和激发态性质现在可以按常规测定，精度很高。在本章中，我们概述了CCM的形式主义，并详细描述了CCM是如何应用的。我们通过展示四种不同自旋模型的结果来说明该方法的功能和通用性。即，XXZ模型，方形晶格上具有不同强度键的海森堡模型，在kagome和三角晶格反铁罗曼星系和方形晶格上受挫的铁磁自旋系统之间进行插值的模型。我们考虑了所有这些系统的基态性质，并给出了自旋半方晶格XXZ模型激发能的精确结果。我们利用一个“扩展”的SUB2近似方案，并演示了如何通过使用傅里叶变换方法精确地解决这个近似，或者通过确定和解决SUB2-m问题。我们还给出了称为LSUBm或SUBm-m格式的“局部”近似格式的结果。我们注意到，我们必须利用计算技术来解决这些“高阶”的局部近似方案。我们证明了我们能够很准确地确定量子相变的位置，并且我们证明了我们能够通过将CCM与相干异常方法（CAM）结合使用来确定它们的量子临界性。此外，我们还说明了CCM可以用于确定晶格量子自旋系统的“节点表面”。最后，我们展示了如何通过使用CCM在LSUBm近似的不同水平上确定自旋半三角晶格反铁磁体的微扰级数来建立与累积级数展开的联系。
The Coupled Cluster Method (CCM) is one of the most powerful and universally applied techniques of quantum many-body theory. In particular, it has been used extensively in order to investigate many types of lattice quantum spin system at zero temperature. The ground-and excited-state properties of these systems may now be determined routinely to great accuracy. In this Chapter we present an overview of the CCM formalism and we describe how the CCM is applied in detail. We illustrate the power and versatility of the method by presenting results for four different spin models. These are, namely, the XXZ model, a Heisenberg model with bonds of differing strengths on the square lattice, a model which interpolates between the Kagome-and triangular-lattice antiferromanets and a frustrated ferrimagnetic spin system on the square lattice. We consider the ground-state properties of all of these systems and we present accurate results for the excitation energies of the spin-half square-lattice XXZ model. We utilise an “extended” SUB2 approximation scheme, and we demonstrate how this approximation may be solved exactly by using Fourier transform methods or, alternatively, by determining and solving the SUB2-m problem. We also present the results of “localised” approximation schemes called the LSUBm or SUBm-m schemes. We note that we must utilise computational techniques in order to solve these localised approximation schemes to “high order.” We show that we are able to determine the positions of quantum phase transitions with much accuracy, and we demonstrate that we are able to determine their quantum criticality by using the CCM in conjunction with the coherent anomaly method (CAM). Also, we illustrate that the CCM may be used in order to determine the “nodal surfaces” of lattice quantum spin systems. Finally, we show how connections to cumulant series expansions may be made by determining the perturbation series of a spin-half triangular-lattice antiferromagnet using the CCM at various levels of LSUBm approximation.