Topological lattice actions
Topological lattice actions
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拓扑晶格作用
DOI：
10.1007/jhep12(2010)020
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发表时间：
2010
影响因子：
5.4
通讯作者：
U. Wiese
中科院分区：
文献类型：
--
作者：
W. Bietenholz;U. Gerber;M. Pepe;U. Wiese
我们考虑具有拓扑作用的晶格场论，它对于场的小变形是不变的。其中一些行为具有分隔不同拓扑部分的无限障碍。拓扑作用没有正确的经典连续谱极限，并且不能使用微扰理论来处理它们，但它们仍然产生正确的量子连续谱极限。为了证明这一点，我们提出了 1-d O(2) 和 O(3) 模型的分析研究，以及使用拓扑晶格作用的 2-d O(3) 模型的蒙特卡罗模拟。一些拓扑作用遵循作用和拓扑电荷 Q 之间的格施瓦茨不等式。无论如何，在 2-d O(3) 模型中，拓扑磁化率 $ {\chi_t} = {{{\left\langle {{Q^2}} \right\rangle }} \left/ {V} \right.} $ 在连续统极限上呈对数发散。尽管如此，在非零距离处，拓扑电荷密度的相关器具有有限的连续极限，这与分析预测一致。我们的研究明确表明，动作的一些经典重要特征与达到正确的量子连续体极限无关。
We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not have the correct classical continuum limit and they cannot be treated using perturbation theory, but they still yield the correct quantum continuum limit. To show this, we present analytic studies of the 1-d O(2) and O(3) model, as well as Monte Carlo simulations of the 2-d O(3) model using topological lattice actions. Some topological actions obey and others violate a lattice Schwarz inequality between the action and the topological charge Q. Irrespective of this, in the 2-d O(3) model the topological susceptibility $ {\chi_t} = {{{\left\langle {{Q^2}} \right\rangle }} \left/ {V} \right.} $ is logarithmically divergent in the continuum limit. Still, at non-zero distance the correlator of the topological charge density has a finite continuum limit which is consistent with analytic predictions. Our study shows explicitly that some classically important features of an action are irrelevant for reaching the correct quantum continuum limit.