层次波函数--从共形关联函数到Tao-non态
Hierarchy wave functions--from conformal correlators to Tao-Thouless states
摘要：
Laughlin的波函数描述了填充因子$ν=1/(2k+1)$下的分数量子霍尔效应，它可以用共形场论中的关联函数得到，最近这种构造被推广到填充因子$ν=n/(2kn+1)$下的Jain复合费米子波函数。在这里，我们概括了后者的建设和目前的基态波函数的所有量子霍尔层次结构的状态，通过连续凝聚的准电子（而不是准空穴）在原来的层次结构。通过考虑这些波函数在一个圆柱，我们表明，他们接近确切的基态，Tao-nesses状态，当圆柱变薄。我们还提出了多空穴态的波函数，使连接到文的阿贝尔量子霍尔流体的一般分类，并讨论是否可以解析确定的准粒子的分数统计。最后讨论了我们的波函数在多大程度上可以用复合费米子的语言来描述。
英文摘要：
Laughlin's wave functions, describing the fractional quantum Hall effect at filling factors $ν=1/(2k+1)$, can be obtained as correlation functions in conformal field theory, and recently this construction was extended to Jain's composite fermion wave functions at filling factors $ν=n/(2kn+1)$. Here we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multi-hole states, make the connection to Wen's general classification of abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally we discuss to what extent our wave functions can be described in the language of composite fermions.
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