非常规填充因子4/11：基态波函数的封闭形式
Unconventional Filling Factor 4/11: A Closed-Form Ground State Wave Function
摘要：
填充因子为4/11时的基态非常好理解[Phys. Rev. Lett. 112，016801（2014）]，其关联类似于相对角动量为3的两体Haldom赝势的基态电子的关联，即$V_3$ .本文提出了填充因子为1/3时$V_3$基态波函数的封闭形式。我们成功地比较了它与精确的波函数的系统与几个电子，通过计算它们的相互重叠，对关联函数，纠缠谱。通过对几个电子系统的数值精确对角化，我们发现非零$V_3$和$V_1$的窗口是4/11态不可压缩的必要条件。用该波函数构造的4/11态的波函数与已研究的复合费米子对角化基态波函数具有令人满意的高重叠性。
英文摘要：
The ground state at 4/11 filling factor is very well understood [Phys. Rev. Lett. 112, 016801 (2014)] in terms of the 1/3 filled second effective Landau level of the composite fermions whose correlations resemble with that of electrons in the ground state of two-body Haldane pseudo-potential of relative angular momentum 3, $V_3$. We here propose a closed-form ground state wave function for $V_3$ at 1/3 filling factor. We successfully compare it with the exact wave function for the systems with a few electrons, by calculating their mutual overlap, pair-correlation function, and entanglement spectra. By numerical exact diagonalization for a few electron systems, we find a window of nonzero $V_3$ is essential together with $V_1$ for being 4/11 state incompressible. The constructed wave function for 4/11 state using this proposed wave function has satisfactorily high overlap with the previously studied composite-fermion-diagonalized ground state wave function.
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