The spin vectors are quantized and may be described picturesquely as a unification of electromagnetism and ``gravity'' in condensed-matter physics.Expand

It is shown that under certain mild assumptions the generalized hierarchy construction exhausts all possible Abelian fractional quantum Hall states and identifies and determines the topological quantity known as the shift.Expand

The ground-state degeneracy provides a new quantum number in addition to the Hall conductance, characterizing different phases of the FQH systems, and the Ginzburg-Landau theory is a dual theory of the U(1) Chern-Simons topological theory.Expand

La dependance de la degenerescence du vide avec la topologie de l'espace reflete une espece de mise en ordre topologique dans l'etat de spin chiral.Expand

The edge excitations are shown to form a new kind of state which is called the Chiral Luttinger Liquid (´LL), which clearly demonstrate the non-Fermi liquid behaviors of the FQH states.Expand

The mean-field theory of a T- and P-symmetric spin-liquid state is developed. The quasiparticle excitations in the spin-liquid state are shown to be spin-1/2 neutral fermions (the spinons) and charge… Expand

It is shown that several different order parameters can be used to characterize a type of P- and T-violating state for spin systems, that are called chiral-spin states, and speculated that superconducting states with unusual values of the flux quantum may exist.Expand

The Fractional Quantum Hall states with non-Abelian statistics are studied and it is argued that the topological orders and the associated properties are robust against any kinds of small perturbations.Expand

It is found that, for strong confining potentials, the edge of a $\nu=1$ liquid is described by the $Z_F=1 $ Fermi Liquid theory, even in the presence of interactions, a consequence of the chiral nature of the system.Expand

Numerical experiments are presented, which provide evidence for several aspects of the theory, and the existence of a novel incompressible quantum liquid for spinless fermions at \ensuremath{\nu}=1/2 in the Hall effect is suggested.Expand