Geometric aspects of quantum spin states
Geometric aspects of quantum spin states
复制标题
量子自旋态的几何方面
DOI：
10.1007/bf02108805
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发表时间：
1993
影响因子：
2.4
通讯作者：
B. Nachtergaele
中科院分区：
文献类型：
--
作者：
M. Aizenman;B. Nachtergaele
借助于系统平衡态的泛函积分表示，分析了量子自旋链基态的一些有趣的特征。在具有相互作用−P(O)的SU(2S+1)不变量子自旋-S链的背景下，介绍了普遍适用的方法，其中P(O)是最近邻自旋对的单重态的投影。这里讨论的现象包括：Néel序的缺失，二聚化的可能性，存在光谱间隙的条件，以及类似于Affleck和Lieb发现的二分法，指出系统要么表现出关联的缓慢衰减，要么表现出平移对称破缺。我们的表示阐明了−P(O)自旋-S系统与另一维的Potts和FortuinKasteleyn随机团簇模型之间的关系，这一点已经在前面找到了证据。该方法揭示了列出的现象的几何方面，并给出了一幅基态图像的精确感觉，在该图像中，自旋被分组为零总自旋的随机星团。例如，在这样的结构中，拓扑论证隐含着二分法，而备选方案对应于簇是否具有有限的平均长度。
A number of interesting features of the ground states of quantum spin chains are analyzed with the help of a functional integral representation of the system's equilibrium states. Methods of general applicability are introduced in the context of the SU(2S+1)-invariant quantum spin-S chains with the interaction −P(o), whereP(o) is the projection onto the singlet state of a pair of nearest neighbor spins. The phenomena discussed here include: the absence of Néel order, the possibility of dimerization, conditions for the existence of a spectral gap, and a dichotomy analogous to one found by Affleck and Lieb, stating that the systems exhibit either slow decay of correlations or translation symmetry breaking. Our representation elucidates the relation, evidence for which was found earlier, of the −P(o) spin-S systems with the Potts and the Fortuin-Kasteleyn random-cluster models in one more dimension. The method reveals the geometric aspects of the listed phenomena, and gives a precise sense to a picture of the ground state in which the spins are grouped into random clusters of zero total spin. E.g., within such structure the dichotomy is implied by a topological argument, and the alternatives correspond to whether, or not, the clusters are of finite mean length.