平移不变纯态及其分裂性质
Translation invariant pure state and its split property
摘要：
本文证明了$\clb = \otimes_{\IZ}M_d(C), \;d \ge 2$上任意平移不变纯态的Haag对偶性，其中$M_d(C)$是复数域上的$d \times d$维矩阵的集合.我们还证明了一个平移不变因子态在$\clb$上是纯的充要条件。这一结果使得研究具有附加对称性的纯态成为可能。本文证明了实格点对称反射正平移不变纯态的两点空间相关函数是指数衰减的分裂态。当$d$为偶数时，$\clb$上不存在实的、格点对称的、正反射的、$su(2)$不变的平移不变纯态.这特别说明，自旋自由度为1/2奇数的海森堡反铁磁体模型在其基态存在自发对称破缺
英文摘要：
We prove Haag duality property of any translation invariant pure state on $\clb = \otimes_{\IZ}M_d(C), \;d \ge 2$, where $M_d(C)$ is the set of $d \times d$ dimensional matrices over field of complex numbers. We also prove a necessary and sufficient condition for a translation invariant factor state to be pure on $\clb$. This result makes it possible to study such a pure state with additional symmetry. We prove that exponentially decaying two point spacial correlation function of a real lattice symmetric reflection positive translation invariant pure state is a split state. Further there exists no translation invariant pure state on $\clb$ that is real, lattice symmetric, refection positive and $su(2)$ invariant when $d$ is an even integer. This in particular says that Heisenberg iso-spin anti-ferromagnets model for 1/2-odd integer spin degrees of freedom admits spontaneous symmetry breaking at it's ground states
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