General topological features and instanton vacuum in quantum Hall and spin liquids
General topological features and instanton vacuum in quantum Hall and spin liquids
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量子霍尔和自旋液体中的一般拓扑特征和瞬子真空
DOI：
10.1103/physrevb.72.035329
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发表时间：
2005
影响因子：
3.7
通讯作者：
N. Surendran
中科院分区：
文献类型：
--
作者：
A. Pruisken;R. Shankar;N. Surendran
我们在量子霍尔液体和自旋液体中引入了超普适的概念。这一概念源于以前对量子霍尔效应的研究，并指出量子霍尔效应的所有基本特征一般表现为二维非线性{sigma}模型中的{theta}参数的一般拓扑特征。为了在自旋液体中建立超普适性，我们回顾了Haldane的映射，他认为1+1时空维的反铁磁性Heisenberg自旋-S链可以用带有{theta}项的O(3)非线性{sigma}模型有效地描述。通过将二聚化自旋S=1/2链的路径积分表示与重整化群抽取技术相结合，我们将霍尔丹方法推广到包含四个不同重整化群参数的更复杂的理论-费米子旋转链。我们展示了如何使用重整化群计算技术来建立费米子转子链和带有{theta}项的O(3)非线性{sigma}模型之间的桥梁。作为映射的一个整体和基本方面，我们建立了链边缘的悬挂自旋的拓扑意义。自旋液体中的边缘自旋在所有方面都与量子霍尔液体中的无质量手征边缘激发相同。我们考虑了自旋链的各种不同的几何形状，如开链和闭链，以及具有偶数和奇数边数的链。我们表明，对于每个不同的几何形状，{theta}项具有明显不同的物理含义。我们将每种情况与拓扑等价的量子霍尔液进行比较。
We introduce the concept of superuniversality in quantum Hall liquids and spin liquids. This concept has emerged from previous studies of the quantum Hall effect and states that all the fundamental features of the quantum Hall effect are generically displayed as general topological features of the {theta} parameter in nonlinear {sigma} models in two dimensions. To establish superuniversality in spin liquids we revisit the mapping by Haldane who argued that the antiferromagnetic Heisenberg spin-s chain in 1+1 space-time dimensions is effectively described by the O(3) nonlinear {sigma} model with a {theta} term. By combining the path integral representation for the dimerized spin s=1/2 chain with renormalization-group decimation techniques we generalize the Haldane approach to include a more complicated theory, the fermionic rotor chain, involving four different renormalization-group parameters. We show how the renormalization-group calculation technique can be used to build a bridge between the fermionic rotor chain and the O(3) nonlinear {sigma} model with the {theta} term. As an integral and fundamental aspect of the mapping we establish the topological significance of the dangling spin at the edge of the chain. The edge spin in spin liquids is in all respects identical to the massless chiral edge excitations in quantummore » Hall liquids. We consider various different geometries of the spin chain such as open and closed chains, chains with an even and odd number of sides. We show that for each of the different geometries the {theta} term has a distinctly different physical meaning. We compare each case with a topologically equivalent quantum Hall liquid.« less