Path integrals, diffusion on SU(2) and the fully frustrated antiferromagnetic spin cluster
Path integrals, diffusion on SU(2) and the fully frustrated antiferromagnetic spin cluster
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SU(2) 上的路径积分、扩散和完全受抑反铁磁自旋簇
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
J. Chalker
中科院分区：
文献类型：
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作者：
P. M. Hogan;J. Chalker
我们研究的路径积分处理的量子力学的一个完全受挫的自旋集群：集群中的每一对自旋的反铁磁海森堡相互作用耦合相等。这样的星系团之所以有趣，部分是因为它们是几何阻挫自旋系统的基石。使用Hubbard-Stratonovich变换解耦的相互作用，玻尔兹曼因子的自旋团簇的时间演化算子的随机变化的磁场中的一个单一的自旋。时间演化算子遵循SU（2）中的随机游走：通过将这种游走从朗之万描述切换到福克-普朗克描述，并计算其端点的概率分布，我们得到配分函数的表达式，作为单个积分的有限和。该计算提供了一个易于分析的辅助场的方法，如在量子蒙特卡罗计算中使用的说明，并可能被扩展到治疗更复杂的挫折自旋系统。
We study the path-integral treatment of the quantum mechanics of a fully frustrated cluster of spins: a cluster in which every pair of spins is coupled equally by antiferromagnetic Heisenberg interactions. Such clusters are interesting partly because they are the building blocks of geometrically frustrated spin systems. Using a Hubbard–Stratonovich transformation to decouple the interactions, the Boltzmann factor for the spin cluster is written in terms of the time-evolution operator for a single spin in a stochastically varying magnetic field. The time-evolution operator follows a random walk in SU(2): by switching from a Langevin to a Fokker–Planck description of this walk and computing the probability distribution of its end-point, we arrive at an expression for the partition function as a finite sum of single integrals. The calculation provides an analytically tractable illustration of the auxiliary field approach, as used in quantum Monte Carlo calculations, and may potentially be extended to treat more complex frustrated spin systems.