Laughlin wave-function and anyon 平=I[(=-=)e =(x+y,) 1<J
= − − k k z i j i j z z e | | / 2 3 2 ( ) z x iy l j j j = ( + )/ Laughlin wave-function and anyon
± flu UX Anyon and fractional statistics
A flux Anyon and fractional statistics
Topological degeneracy for the abelian topological orders &s Topological degeneracy on a torus (periodic boundary condition is always q
❖ Topological degeneracy on a torus (periodic boundary condition) is always q Topological degeneracy for the Abelian topological orders
Topological degeneracy for FQH states &o The topological degeneracy is determined by the genus of the riemann surface, N ≤a8 ☆ g is the genus
❖ The topological degeneracy is determined by the genus of the Riemann surface, ❖ g is the genus Topological degeneracy for FQH states g N = q
Edge states The electrons are confined in a 2D space Chiral Luttinger liquid massless. relativitistic
Edge states Chiral Luttinger liquid → massless, relativitistic The electrons are confined in a 2D space