论文标题
5/2量子厅效应的Hafnian pH-Pfaffian状态
A Hafnian PH-Pfaffian State for 5/2 Quantum Hall Effect
论文作者
论文摘要
具有1/2中央电荷的pH-PFAFFIAN状态与5/2分数量子厅系统的热霍尔电导测量一致，但缺乏现有数值结果的支持。在本文中，我们提出了一种通过将hafnian因子乘以pH-PFAFFIAF函数来获得的波函数描述的新状态。我们称这个新州为哈夫尼亚pH-pfaffian国家。在球形几何形状中，hafnian pH-Pfaffian状态具有与Pfaffian状态相同的磁通量，从而可以在两种状态之间进行直接的数值比较。在第二个Landau级别中有限系统确切的对角线化的结果表明，与Hafnian pH-Pfaffian状态的确切基态的重叠超过了PFAFFIAN状态，当库仑相互作用的短距离成分增加到一定水平，将数值支持借给Hafnian ph-pfaffian国家。我们进一步表明，hafnian pH-Pfaffian国家在数学上与新提出的压缩pH-Pfaffian国家[Arxiv：2001.01915（2020）]相同，该状态是通过“压缩” pH-Pfaffian状态而形成的，其中有两个Flux Quanta移除，以创建两个Abelian Laughlin type型Quassiparticle，以创建另一个最高范围的Abelian Laughlin type Quasiparticle。结果，我们认为Hafnian pH-Pfaffian状态具有与pH-Pfaffian状态相同的中心电荷，因此与热室电导测量值一致。最后，我们对两个新的波形函数提出了数值结果，这是通过将相对角动量增加的两个pH-Pfaffian态的配对复合费物增加的相对角动量形成的。
The PH-Pfaffian state having 1/2 central charge is consistent with the thermal Hall conductance measurement of 5/2 fractional quantum Hall system, but lacks support from the existing numerical results. In this paper we propose a new state described by a wavefunction obtained by multiplying a Hafnian factor to a PH-Pfaffian wavefunction. We call this new state the Hafnian PH-Pfaffian state. In spherical geometry, the Hafnian PH-Pfaffian state has the same magnetic flux number as the Pfaffian state, allowing a direct numerical comparison between the two states. Results of exact diagonalization of finite systems in the second Landau level show that the overlap of the exact ground state with the Hafnian PH-Pfaffian state exceeds that with the Pfaffian state when the short range component of the Coulomb interaction increases to a certain level, lending a numerical support to the Hafnian PH-Pfaffian state. We further show the Hafnian PH-Pfaffian state is mathematically identical to the newly proposed compressed PH-Pfaffian state [arxiv: 2001.01915 (2020)] formed by "compressing" the PH-Pfaffian state with two flux quanta removed to create two abelian Laughlin type quasiparticles of the maximum avoidance from one another. As the result we argue that the Hafnian PH-Pfaffian state has the same central charge as the PH-Pfaffian state, and is therefore consistent with the thermal Hall conductance measurement. Finally we present numerical results on two new wavefunctions formed by increasing the relative angular momentum by two for each of the paired composite fermions of the PH-Pfaffian state.
