论文标题
晶格Quasielectron波函数的连续限
Continuum limit of lattice quasielectron wavefunctions
论文作者
论文摘要
审判国家描述了劳林州的任何Quasiholes，很早就发现了，因此很自然地期望人们也应该能够创建任何Quasielectrons。然而，现有的quasielectrons的试验波函数显示出与预期拓扑特性或其构建不兼容的行为涉及临时元素。但是，表明对于晶格分数量子霍尔系统，可以找到具有所有预期特性的相对简单的quasielectron波函数[new J. Phys。 20，033029（2018）]。这自然提出了一个问题：在连续限制中，这种波函数会发生什么？在这里，我们证明，尽管当quasielectron位于晶格位置的顶部时，人们获得了有限的连续波函数，但通常不存在这种晶格quasielectron的限制。特别是，如果在晶格位点以外的其他地方放置了Quasielectron，则在接近连续性限制时晶格波函数会发出差异。可以通过以最低的兰道级预测国家来消除差异，但我们发现预计的状态也没有任何对任何Quasielectrons的属性。因此，我们得出的结论是，晶格Quasielectron波函数不能解决为连续体中任何一个Quasielectrons寻找试验状态的困难。
Trial states describing anyonic quasiholes in the Laughlin state were found early on, and it is therefore natural to expect that one should also be able to create anyonic quasielectrons. Nevertheless, the existing trial wavefunctions for quasielectrons show behaviors that are not compatible with the expected topological properties or their construction involves ad hoc elements. It was shown, however, that for lattice fractional quantum Hall systems, it is possible to find a relatively simple quasielectron wavefunction that has all the expected properties [New J. Phys. 20, 033029 (2018)]. This naturally poses the question: what happens to this wavefunction in the continuum limit? Here we demonstrate that, although one obtains a finite continuum wavefunction when the quasielectron is on top of a lattice site, such a limit of the lattice quasielectron does not exist in general. In particular, if the quasielectron is put anywhere else than on a lattice site, the lattice wavefunction diverges when the continuum limit is approached. The divergence can be removed by projecting the state on the lowest Landau level, but we find that the projected state does also not have the properties expected for anyonic quasielectrons. We hence conclude that the lattice quasielectron wavefunction does not solve the difficulty of finding trial states for anyonic quasielectrons in the continuum.
