论文标题
使用蒙特卡洛方法的预测分数量子厅状态的真实空间纠缠光谱
Real-space entanglement spectra of projected fractional quantum Hall states using Monte Carlo methods
论文作者
论文摘要
量子大厅（QH）波函数的真实空间纠缠频谱（RSE）提供了一种自然的途径来推断其边缘激发的性质。随着颗粒数量的增加，RSE的计算变得昂贵，并包括Landau级别（LL）。可以使用Monte Carlo（MC）方法对RSE进行有效计算，用于试验状态，这些方法可以写为诸如复合费米（CF）和Parton状态之类的决定因素的产品。该计算效率也适用于最低的Landau级别（LLL）的RSE；但是，这里要使用的LLL投影需要概括Ja那教Kamilla（JK）投影的近似值。这项工作仔细研究了如何进行这种近似。我们通过将MC结果与从计算昂贵但精确的方法中获得的RSE进行比较，确定了最接近JK投影的近似值，并对投影中涉及的近似值进行测试。我们介绍了这些技术，并使用它们来计算确切的LLL投影玻色粒Jain $ 2/3 $的确切rs，该系统的尺寸系统的两部分最高$ n = 24 $。对于RSE的最低角动量部门，我们提供了证据表明MC结果与精确光谱非常匹配。我们还讨论了其他合理的投影方案。我们还计算了未投影的费米尼Jain Jain $ 2/5 $状态，该状态是从球体上两个最低LLS中的Trugman-Kivelson Hamiltonian的精确对角线获得的。通过与Monte Carlo方法的未投影$ 2/5 $状态的RSE进行比较，我们表明后者实际上是准确的。
Real-space entanglement spectrum (RSES) of a quantum Hall (QH) wavefunction gives a natural route to infer the nature of its edge excitations. Computation of RSES becomes expensive with an increase in the number of particles and included Landau levels (LL). RSES can be efficiently computed using Monte Carlo (MC) methods for trial states that can be written as products of determinants such as the composite fermion (CF) and parton states. This computational efficiency also applies to the RSES of lowest Landau level (LLL) projected CF and parton states; however, LLL projection to be used here requires approximations that generalize the Jain Kamilla (JK) projection. This work is a careful study of how this approximation should be made. We identify the approximation closest in spirit to JK projection and perform tests of the approximations involved in the projection by comparing the MC results with the RSES obtained from computationally expensive but exact methods. We present the techniques and use them to calculate the exact RSES of the exact LLL projected bosonic Jain $2/3$ state in bipartition of systems of sizes up to $N=24$ on the sphere. For the lowest few angular momentum sectors of the RSES, we present evidence to show that MC results closely match the exact spectra. We also discuss other plausible projection schemes. We also calculate the exact RSES of the unprojected fermionic Jain $2/5$ state obtained from the exact diagonalization of the Trugman-Kivelson Hamiltonian in the two lowest LLs on the sphere. By comparing with the RSES of the unprojected $2/5$ state from Monte Carlo methods, we show that the latter is practically exact.
