Composite fermions on a torus
Composite fermions on a torus
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环面上的复合费米子
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Jainendra K. Jain
中科院分区：
文献类型：
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作者：
Songyang Pu;Ying;Jainendra K. Jain
我们实现了一个明确的结构的最低朗道水平（LLL）的投影波函数的复合费米子在周期（环面）几何。为此，我们首先演示了如何涡附着的复合费米子（CF）理论可以完成在环面几何产生的“未投影”波函数满足正确的（准）周期性边界条件。然后，我们考虑两种方法将这些波函数投影到LLL。直接投影产生有效的波函数，但只能用于非常小的系统。更强大和更有用的投影方法的Jain和Kamilla失败的环面几何，因为它不保持周期性的边界条件，从而使我们离开原来的希尔伯特空间。我们已经成功地构建了一个修改的投影方法，是一致的周期性边界条件和CF理论的一般结构。这种方法适用于复合费米子的一大类态，称为“固有态”，其中包括电子填充因子为
u=frac{n}{2 pn + 1}$，它们的带电和中性激发，以及在任意填充因子下的准边生成基态，
u=frac{
u^*}{2p
u^*+ 1}$，其中$n$和$p$是整数，$
u^*$是CF填充因子。在填充因子下，与已知的小系统基态和激发态的精确结果进行比较。
u=1/3、2/5和3/7表明我们的LLL投影波函数是实际库仑本征态的非常精确的表示。我们的结构使研究大型系统的复合费米子的环面，从而打开了调查许多有趣的问题和现象的可能性。
We achieve an explicit construction of the lowest Landau level (LLL) projected wave functions for composite fermions in the periodic (torus) geometry. To this end, we first demonstrate how the vortex attachment of the composite fermion (CF) theory can be accomplished in the torus geometry to produce the "unprojected" wave functions satisfying the correct (quasi-)periodic boundary conditions. We then consider two methods for projecting these wave functions into the LLL. The direct projection produces valid wave functions but can be implemented only for very small systems. The more powerful and more useful projection method of Jain and Kamilla fails in the torus geometry because it does not preserve the periodic boundary conditions and thus takes us out of the original Hilbert space. We have succeeded in constructing a modified projection method that is consistent with both the periodic boundary conditions and the general structure of the CF theory. This method is valid for a large class of states of composite fermions, called "proper states," which includes the incompressible ground states at electron filling factors $
u=frac{n}{2pn+ 1}$, their charged and neutral excitations, and also the quasidegenerate ground states at arbitrary filling factors of the form $
u=frac{
u^*}{2p
u^*+ 1}$, where $n$ and $p$ are integers and $
u^*$ is the CF filling factor. Comparison with exact results known for small systems for the ground and excited states at filling factors $
u=1/3$, 2/5 and 3/7 demonstrates our LLL-projected wave functions to be extremely accurate representations of the actual Coulomb eigenstates. Our construction enables the study of large systems of composite fermions on the torus, thereby opening the possibility of investigating numerous interesting questions and phenomena.