Strongly correlated quantum systems in low dimensions often exhibit novel quantum ordering. This ordering is sometimes hidden and can be revealed only by examining new ‘dual’ types of correlations. Such ordering leads to novel collective modes and fractional quantum numbers. Examples will be presented from quantum spin chains and the quantum Hall effect.

The “exotic” particle model associated with the two-parameter central extension of the planar Galilei group can be used to derive the ground states of the Fractional Quantum Hall Effect. Similar equations arise for a semiclassical Bloch electron. Exotic Galilean symmetry is also be shared by Chern-Simons field theory of the Moyal type.

Quasiparticles of the fractional quantum Hall systems obey fractional (including mutual) exclusion statistics. In this note we study the effects of exclusion statistics on thermal activation of quasiparticle pairs in the approximation of generalized ideal gas. The distribution function for thermally activated quasiparticles is found explicitly for the statistics matrix given by the composite fe...

We discuss in many details two quantum mechanical models of planar electrons which are very much related to the Fractional Quantum Hall Effect. In particular, we discuss the localization properties of the trial ground states of the models starting from considerations on the numerical results on the energy. We conclude that wavelet theory can be conveniently used in the description of the system...

The observation of the quantum anomalous Hall effect in a ferromagnetic topological insulator, first reported by experimenters in Beijing last year[1], has attracted considerable attention, including a Journal Club Commentary by Leonid Glazman in July 2013. The new e-print by Checkelsky et al. reports experiments by a Japanese group, which further explore the properties of this fascinating syst...

Taking advantage of the two-parameter central extension of the planar Galilei group, we construct a non relativistic particle model in the plane. Owing to the extra structure, the coordinates do not commute. Our model can be viewed as the non-relativistic counterpart of the relativistic anyon considered before by Jackiw and Nair. For a particle moving in a magnetic field perpendicular to the pl...

We analyze the action of the inhomogeneous modular group Γ(2) on the three cusps of its principal fundamental domain in the Poincaré half plane. From this, we obtain an exhaustive classification of the fractional quantum Hall numbers. This classification is somehow similar to the one given by Jain. We also present some resulting remarks concerning direct phase transitions between the different ...

Wave functions describing quasiholes and electrons in nonabelian quantum Hall states are well known to correspond to conformal blocks of certain coset conformal field theories. In this paper we explicitly analyse the algebraic structure underlying the braiding properties of these conformal blocks. We treat the electrons and the quasihole excitations as localised particles carrying charges relat...

We show that the notion of mutual statistics arises naturally from the representation theory of the braid group over the multi-sheeted surface. A Hamiltonian which describes particles moving on the double-sheeted surface is proposed as a model for the bilayered fractional quantum Hall effect (FQHE) discovered recently. We explicitly show that the quasi-holes of the bilayered Hall fluid display ...

The spin Hall effect depends crucially on the intrinsic spin-orbit coupling of the energy band. Because of the smaller spin-orbit coupling in silicon, the spin Hall effect is expected to be much reduced. We show that the electric field in p-doped silicon can induce a dissipationless orbital current in a fashion reminiscent of the spin Hall effect. The vertex correction due to impurity scatterin...