Field-theoretical methods in quantum magnetism
Field-theoretical methods in quantum magnetism
复制标题
量子磁学中的场论方法
DOI：
10.1007/bfb0119596
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发表时间：
2004
影响因子：
7.7
通讯作者：
P. Pujol
中科院分区：
文献类型：
--
作者：
D. Cabra;P. Pujol
本文综述了在低维量子磁体研究中已证明非常有用的各种场论方法。首先回顾了自旋波分析和非线性σ模型方法在一维和二维量子反铁磁体中的应用。我们讨论特别是出现的Halflit的猜想自旋链和梯子在这种形式主义。本文还简要讨论了二维正方晶格反铁磁体的非线性σ模型描述。在第二部分中，我们回顾了阿贝尔玻色化方法及其在XXZ自旋1/2链及其推广，如二聚化链研究中的应用。非阿贝尔玻色化被用来描述具有任意自旋S的SU（2）对称链和2个梯形腿，在这种形式下重新推导了Haldman猜想。还讨论了导致哈伯德或t-J模型的电荷自由度的列入。最后，我们将阿贝尔玻色化方法应用于无磁场中的N脚阶梯的研究，从而进一步推广了Halfman猜想。
We present a review of different field theory techniques that have proved very useful in the study of quantum magnets in low dimensions We first review the application of the spin-wave analysis and non-linear σ-model techniques in one and two dimensional quantum antiferromagnets. We discuss in particular the emergence of Haldane’s conjecture for spin chains and ladders within this formalism. We also present a brief discussion on the non-linear σ-model description for the two-dimensional antiferromagnet in the square lattice. In a second part we review the method of abelian bosonization and its application to the study of the XXZ spin 1/2 chain and its generalizations, such as the dimerized chain. Non-abelian bosonization is used to describe both SU (2) symmetric chains with arbitrary spin S and 2 leg ladders, rederiving Haldane’s conjecture within this formalism. The inclusion of charge degrees of freedom leading to a Hubbard or a t—J model is also discussed. Finally, we apply the abelian bosonization approach to the study of N-leg ladders in amagnetic field, which leads to a further extension of Haldane’s conjecture.