This book presents the high-precision analysis of ground states and
low-energy excitations in fractional quantum Hall states formed by Dirac
electrons, which have attracted a great deal of attention. In particular
the author focuses on the physics of fractional quantum Hall states in
graphene on a hexagonal boron nitride substrate, which was recently
implemented in experiments. The numerical approach employed in the book,
which uses an exact numerical diagonalization of an effective model
Hamiltonian on a Haldane's sphere based on pseudopotential
representation of electron interaction, provides a better understanding
of the recent experiments.
The book reviews various aspects of quantum Hall effect: a brief
history, recent experiments with graphene, and fundamental theories on
integer and fractional Hall effects. It allows readers to quickly grasp
the physics of quantum Hall states of Dirac fermions, and to catch up on
latest research on the quantum Hall effect in graphene.