A geometrical look of the fractional quantum Hall effect

Fractional quantum Hall (FQH) states are archetypes of strongly correlated topological phases of matter. These states can be characterized by localized excitations with fractional charge, fractional and possibly nonabelian statistics, gapless edge modes, and nontrivial entanglement spectra. Our understanding of the FQH states mostly relies on the "variational" approach pioneered by Laughlin, whose wavefunction nevertheless has no variational parameter. In this talk I explain how one can write down a family of wavefunctions with identical topological characteristics, but with different geometrical information, encoded in the so-called guiding-center metric, which was proposed by Haldane [Phys. Rev. Lett. 107, 116801 (2011)]. For illustration, we introduce generalized model wavefunctions for a FQH system with anisotropic interaction. The variation of the guiding-center metric and the breakdown of the anisotropic FQH state will be discussed.