Nonabelions in the fractional quantum hall effect

TLDR

Conformal field theory is applied to fractional quantum Hall systems, interpreting Laughlin wave functions and related states as conformal blocks of rational CFTs. The authors construct an exactly solvable electron Hamiltonian whose ground state and quasihole excitations exhibit nonabelian statistics, introducing the term “nonabelions”. They build a Hamiltonian based on conformal field theory that yields a known ground state and nonabelian quasihole excitations. The study shows that fractional quantum Hall universality classes are defined by excitation quantum numbers and statistics, linking order parameters to chiral algebras and proposing new order parameters for several states.

Abstract

Applications of conformal field theory to the theory of fractional quantum Hall systems are discussed. In particular, Laughlin's wave function and its cousins are interpreted as conformal blocks in certain rational conformal field theories. Using this point of view a hamiltonian is constructed for electrons for which the ground state is known exactly and whose quasihole excitations have nonabelian statistics; we term these objects “nonabelions”. It is argued that universality classes of fractional quantum Hall systems can be characterized by the quantum numbers and statistics of their excitations. The relation between the order parameter in the fractional quantum Hall effect and the chiral algebra in rational conformal field theory is stressed, and new order parameters for several states are given.