Field Theory for Fractional Quantum Hall States
Field Theory for Fractional Quantum Hall States
复制标题
分数量子霍尔态的场论
DOI：
10.1103/physrevb.92.235141
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Paul Wiegmann
中科院分区：
文献类型：
--
作者：
T. Can;M. Laskin;Paul Wiegmann
我们发展了分数量子霍尔态的场论描述。我们证明了在梯度展开的前导近似下，Laughlin态可用具有背景电荷的高斯自由场理论来描述，背景电荷与态的反常粘性相一致。背景电荷使相应的共形场论的中心电荷增加到1以上，类似于二维量子引力理论的中心电荷。紫外线正则化对高斯场理论的梯度修正反映了引力异常。它们也与量子引力的刘维尔理论有关。我们展示了场作用的梯度展开如何编码FQH效应的普遍特征，而不是霍尔电导。这种方法为计算弯曲空间中FQHE的引力异常和关联函数提供了一种比作者在以前的论文中采用的迭代Ward恒等式的方法更透明和有用的方法。
We develop a field theory description of fractional quantum Hall (FQH) states. We show that in the leading approximation in a gradient expansion, Laughlin states are described by a Gaussian free field theory with a background charge which is identified with the anomalous viscosity of the states. The background charge increases the central charge of the corresponding conformal field theory above 1, similar to that of the theory of 2D quantum gravity. Gradient corrections to the Gaussian field theory arising from ultraviolet regularization reflect the gravitational anomaly. They are also related to the Liouville theory of quantum gravity. We show how the gradient expansion of the field action encodes the universal features of the FQH effect beyond that of Hall conductance. This method provides a more transparent and useful alternative for computing the gravitational anomaly and correlation functions of the FQHE in a curved space than the method of iterating the Ward identity employed by the authors in previous papers.