Generalized Laughlin\'s Theory for the Fractional Quantum Hall Effect

Strong correlation between electrons in two dimensional electron systems subjected to large magnetic field at low temperature produces a topological quantum liquid that is manifested through the phenomenon of fractional quantum Hall effect in which Hall resistance quantizes at some specific values. Based on general principles, Laughlin proposed a manybody wavefunction which is an excellent description for the filling factors 1/m (m odd), but its any kind of generalization fails to describe states at other filling factors with similar confidence. In this talk, I will describe, starting from a Laughlin wavefunction, a simple and elegant scheme for constructing manybody wavefunctions for other fractional quantum Hall states as coupled Laughlin condensates present in different Hilbert subspaces spanned by different set of analytic functions. Surprisingly, these simple form of the wavefunctions are identical with the wavefunctions proposed in composite fermion theory which is based on a key postulate that the electrons form a bound state with even number of quantum vortices, making themselves composite fermions, and these composite fermions qualify to produce integer quantum Hall state.