A Novel Conformal Field Theory Approach to Bulk Wave Functions in the Fractional Quantum Hall Effect

In this thesis, a novel approach is proposed to represent bulk wave functions of fractional quantum HALL states in terms of conformal field theory correlators. It starts from the LAUGHLIN states and their generalization following JAIN’s picture of composite fermions. These effective particles are naturally identified within the b/c-spin conformal field theories. The enigmatic phenomenon of fractional statistics is described by twist fields which inherently appear in the spin systems. A geometrical interpretation is obtained in which bulk wave functions are understood as holomorphic functions over a ramified covering of the complex plane. To extend JAIN’s main series, the concept of composite fermions that pair to spin singlets is introduced. This is naturally adopted by the particular b/c-spin system with central charge c=−2 as known for the HALDANE-REZAYI state with filling fraction ν = 5/2. In this way, the new conformal field theory proposal covers the set of experimentally confirmed fractional quantum HALL states in the lowest LANDAU level. Concerning their stability with respect to energy gaps of the ground states, a natural ordering is deduced where unobserved filling fractions are precisely avoided. The scheme is compatible with classifications in terms of effective CHERN-SIMONS theories. It leads to severe restrictions of the coupling K-matrices and, in addition, the b/c-spin approach can be extended to describe non-ABELIAN fractional quantum HALL states imposing physical constraints on them. The scientific results underlying this thesis are submitted for publication to Phys. Rev. B and can be found in [72].