多分量量子Hall系统的Chern-Simons理论
Chern-Simons theory of multi-component quantum Hall systems
摘要：
Chern-Simons方法已被广泛用于在试探波函数框架下解释分数量子霍尔态。在本文中，我们概括了陈-西蒙斯变换的概念，系统与任何数量的组件（自旋或pseudospin自由度），扩展早期的结果与一个或两个组件的系统。我们通过加入辅助规范场和适当的约束来处理密度涨落。在这些领域的哈密顿量是二次的，因此可以被视为一个谐振子哈密顿量，通过等离子体类比与Halperin波函数连接的基态。我们调查的Chern-Simons变换的系数和填充因子，我们的模型是有效的几个条件。此外，我们讨论了几个奇异的情况下，与对称状态。
英文摘要：
The Chern-Simons approach has been widely used to explain fractional quantum Hall states in the framework of trial wave functions. In the present paper, we generalise the concept of Chern-Simons transformations to systems with any number of components (spin or pseudospin degrees of freedom), extending earlier results for systems with one or two components. We treat the density fluctuations by adding auxiliary gauge fields and appropriate constraints. The Hamiltonian is quadratic in these fields and hence can be treated as a harmonic oscillator Hamiltonian, with a ground state that is connected to the Halperin wave functions through the plasma analogy. We investigate several conditions on the coefficients of the Chern-Simons transformation and on the filling factors under which our model is valid. Furthermore, we discuss several singular cases, associated with symmetric states.
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