Lieb-Schultz-Mattis in higher dimensions
Lieb-Schultz-Mattis in higher dimensions
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DOI：
10.1103/physrevb.69.104431
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发表时间：
2004-03-01
影响因子：
3.7
通讯作者：
Hastings, MB
中科院分区：
文献类型：
--
作者：
Hastings, MB
将Lieb-Schultz-Mattis定理推广到高维自旋系统。这一结果的物理动机是，这种自旋系统通常要么具有长程有序，在这种情况下有无间隙模，要么只有短程关联，在这种情况下，有拓扑激发。结果使用了一组循环算符，类似于规范理论中使用的那些，根据该理论的自旋算符定义。我们还得到了有间隙系统的期望值的各种聚类界。在间隙假设下，这些界限被用来排除长程有序的第一种情况，之后我们证明了拓扑激发的存在。与基态相比，拓扑激发态对于作用在任何局部区域内的所有算符具有相同的期望值，但具有不同的动量。
A generalization of the Lieb-Schultz-Mattis theorem to higher-dimensional spin systems is shown. The physical motivation for the result is that such spin systems typically either have long-range order, in which case there are gapless modes, or have only short-range correlations, in which case there are topological excitations. The result uses a set of loop operators, analogous to those used in gauge theories, defined in terms of the spin operators of the theory. We also obtain various cluster bounds on expectation values for gapped systems. These bounds are used, under the assumption of a gap, to rule out the first case of long-range order, after which we show the existence of a topological excitation. Compared to the ground state, the topologically excited state has, up to a small error, the same expectation values for all operators acting within any local region, but it has a different momentum.