Screening properties of quasielectrons in Laughlin states*

I review recent work on how to construct a matrix product state representation of quasielectron excitations of Laughlin QH wave functions. These, which are obtained, either by using composite fermions, or conformal field theory, have a known defect - the the positions of the quasielectrons depend on the presence of other quasiparticles even when these are far removed. This poses a serious problem since the braiding phases of the quasiparticles are not correct which signifies that the states do not have correct topological properties. This failure is analyzed in detail and is shown to arise because of an incomplete screening which causes the plasma analogy. We discuss various ways to overcome the problems by adding screening operators.