Analysis of Quantum Spin Systems by a Nonlinear Sigma Model Method

用非线性西格玛模型方法分析量子自旋系统

基本信息

批准号：
14540366
负责人：
TAKANO Ken'ichi
金额：
$ 0.64万
依托单位：
Toyota Technological Institute
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540366/
关键词：
quantum spin system Heisenberg model nonlinear sigma model side chain disordered state antiferromagnetism spin-gap frustration J1-J2模型反強磁性秩序 J_1-J_2模型ハイゼンベルク模型

项目摘要

In a quantum spin system with antiferromagnetic interactions, strong quantum fluctuation may destroy the spin order so as to form a disordered ground state. Then a spin excitation from the ground state has a finite excitation energy or spin-gap. We formulated a novel nonlinear σ model method and, by using it, we examined disordered states for quantum spin systems.Especially, we established a nonlinear σ model method for a spin system with first- and second-neighbor exchange interactions on a square lattice, which is called the J1-J2 Heisenberg model. Based on the formulation and assisted by some known results, we found that the ground state of this model is the plaquette state in the disordered phase.The formulation can be extended, in priciple, to another two-dimensional spin system, if its classical version has an antiferromagnetic spin order. We examined the cases of a triangular lattice with square-lattice-like anisotropy and a honycomb lattice. The characters of the disorderd ground states are issues. The ground state for an anisotropic triangular lattice near a square lattice continues to that for a sqare lattice, meaning that their disordered state is basically the same.On the other hand, the nonlinear σ model method for a system with strong frustration is not established yet. In the case of strong frustration, the classical version of a quantum spin system has, for example, an order of 120-degree structure and not an antiferromagnetic order. The extention of the nonlinear σ model method to such a system is not easy. We have done some trials for a general formulation.For one-dimensional quantum spin systems, we extend the nonlinear σ model method to the case of spins with side chains. The condition for having gapless spin excitations is changed from the case of no side chains.

在具有抗磁相互作用的量子自旋系统中，强量子波动可能会破坏自旋顺序，从而形成无序的基态。然后，来自基态的自旋兴奋具有有限的激动人心的能量或自旋隙。我们制定了一种新型的非线性σ模型方法，并通过使用它来检查无序状态的量子自旋系统。尤其是，我们建立了一种非线性σ模型方法，用于在平方晶格上具有一定序和第二个邻居交换相互作用的自旋系统，该方法称为J1-J2 Heisenberg模型。基于公式并获得了一些已知结果的辅助，我们发现该模型的基态是无序阶段的plaquette状态。如果其经典版本具有抗Fiferromagagnetic Spin Order，则可以将公式以价格扩展到另一个二维自旋系统。我们检查了带有方形晶格的三角形晶格的病例和霍尼科姆晶格。无序基础状态的特征是问题。平方晶格附近的各向异性三角晶格的基态继续存在，这意味着它们的无序状态基本上是相同的。另一方面，尚未确定具有强挫折系统的非线性σ模型方法。在强烈挫败感的情况下，量子自旋系统的经典版本具有120度结构的阶，而不是反铁磁序。将非线性σ模型方法扩展到这种系统并不容易。我们已经对通用公式进行了一些试验。对于一维量子自旋系统，我们将非线性σ模型方法扩展到带有侧链的旋转情况。没有侧链的情况，具有无间隙旋转兴奋的条件发生了变化。