We review various features of interacting Abelian topological phases of matter in two spatial
dimensions, placing particular emphasis on fractional Chern insulators (FCIs) and fractional …

We develop a first quantization description of fractional Chern insulators that is the dual of
the conventional fractional quantum Hall (FQH) problem, with the roles of position and …

It was recently pointed out that topological liquid phases arising in the fractional quantum
Hall effect (FQHE) are not required to be rotationally invariant, as most variational wave …

The topological physics of quantum Hall states is efficiently encoded in purely topological
quantum field theories of the Chern-Simons type. The reliable inclusion of low-energy …

As lattice analogs of fractional quantum Hall systems, fractional Chern insulators (FCIs)
exhibit enigmatic physical properties resulting from the intricate interplay between single …

We derive an effective field theory for the isotropic-nematic quantum phase transition of
fractional quantum Hall states. We demonstrate that for a system with an isotropic …

We elucidate the nature of neutral collective excitations of fractional quantum Hall liquids in
the long-wavelength limit. We demonstrate that they are chiral gravitons carrying angular …

Geometric fluctuations of the density mode in a fractional quantum Hall (FQH) state can give
rise to a nematic FQH phase, a topological state with a spontaneously broken rotational …

The fractional quantum Hall state at the Landau level filling factor 5/2 is extremely interesting
because it is likely the first non-Abelian state, but its precise nature remains unclear after …

Understanding the quantum problem of a free charged particle undergoing two-dimensional
motion in a perpendicular uniform, constant magnetic field is necessary to the …