Department of Mathematical Physics, National University of Ireland, Maynooth, Ireland.
Phys Rev Lett. 2012 Jun 22;108(25):256806. doi: 10.1103/PhysRevLett.108.256806. Epub 2012 Jun 19.
We devise a way to calculate the dimensions of symmetry sectors appearing in the particle entanglement spectrum (PES) and real space entanglement spectrum (RSES) of multiparticle systems from their real space wave functions. We first note that these ranks in the entanglement spectra equal the dimensions of spaces of wave functions with a number of particles fixed. This also yields equality of the multiplicities in the PES and the RSES. Our technique allows numerical calculations for much larger systems than were previously feasible. For somewhat smaller systems, we can find approximate entanglement energies as well as multiplicities. We illustrate the method with results on the RSES and PES multiplicities for integer quantum Hall states, Laughlin and Jain composite fermion states, and for the Moore-Read state at filling ν = 5/2 for system sizes up to 70 particles.
我们设计了一种方法，从多粒子系统的实空间波函数中计算出在粒子纠缠谱（PES）和实空间纠缠谱（RSES）中出现的对称扇区的尺寸。我们首先注意到，这些纠缠谱中的秩等于粒子数固定的波函数空间的维数。这也使得 PES 和 RSES 中的多重性相等。我们的技术允许对比以前更可行的更大系统进行数值计算。对于稍小的系统，我们还可以找到近似的纠缠能以及多重性。我们用整数量子霍尔态、Laughlin 和 Jain 复合费米子态以及填充比为 ν = 5/2 的 Moore-Read 态的 RSES 和 PES 多重性的结果来说明该方法，系统大小高达 70 个粒子。
