Quantum fluctuations in quantum lattice systems with continuous symmetry
Quantum fluctuations in quantum lattice systems with continuous symmetry
复制标题
连续对称量子晶格系统中的量子涨落
DOI：
10.1007/bf02175562
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发表时间：
1996
影响因子：
1.6
通讯作者：
T. Momoi
中科院分区：
文献类型：
--
作者：
T. Momoi
我们讨论了在 T=0 时量子晶格系统中不存在连续对称性自发破坏的条件。我们的分析基于 Pitaevskii 和 Stringari 的想法，即不确定性关系可以用来显示量子涨落。对于一维系统，如果某个均匀磁化率是有限的，则基态在连续变换下是不变的。对于二维和三维系统，研究表明，只要连续对称性自发破缺，截断相关函数的衰减速度就不会比|r|−d+1 更快。这两种现象都是由于量子涨落而发生的。我们的定理涵盖了一系列具有不太长程相互作用的量子晶格系统。
We discuss conditions for the absence of spontaneous breakdown of continuous symmetries in quantum lattice systems atT=0. Our analysis is based on Pitaevskii and Stringari's idea that the uncertainty relation can be employed to show quantum fluctuations. For one-dimensional systems, it is shown that the ground state is invariant under a continuous transformation if a certain uniform susceptibility is finite. For the two- and three-dimensional systems, it is shown that truncated correlation functions cannot decay any more rapidly than|r|−d+1whenever the continuous symmetry is spontaneously broken. Both of these phenomena occur owing to quantum fluctuations. Our theorems cover a wide class of quantum lattice systems having not-too-long-range interactions.