Related papers: The Quantum Hall Effect in Supersymmetric Chern-Si…
We build the constraint that all electrons are in the lowest Landau level into the Chern-Simons field theory approach for the fractional quantum Hall system. We show that the constraint can be transmitted from one hierarchical state to the…
We present a Chern-Simons matrix model describing the fractional quantum Hall effect on the two-sphere. We demonstrate the equivalence of our proposal to particular restrictions of the Calogero-Sutherland model, reproduce the quantum states…
In (2+1) dimensions, the Maxwell term $-(1/4) F_{\alpha\beta}F^{\alpha\beta}$ can be replaced by the Chern-Simons three-form $(\kappa/4)\epsilon^{\alpha\beta\gamma}A_\alpha F_{\beta\gamma}$, yielding a novel type of `electromagnetism'. This…
We consider the non-relativistic Chern-Simons equations proposed by Zhang, Hansen and Kivelson as the mean field theory of the fractional Hall effect. We prove the existence of the vortex lattice solutions (i.e. solution with lattice…
We construct effective field theories of the quantum skyrmion Hall effect from matrix Chern-Simons theory for $N$ electrons, corresponding to matrix dimension $N$. We first consider a quantum Hall droplet within finite $N$ matrix…
We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.…
We study Maxwell-Chern-Simons theory in 2 noncommutative spatial dimensions and 1 temporal dimension. We consider a finite matrix model obtained by adding a linear boundary field which takes into account boundary fluctuations. The pure…
These pedagogical lecture notes present a general introduction to most aspects of the integer and fractional quantum Hall effects. This is followed by an extensive discussion of quantum Hall ferromagnetism, both for spins in single-layer…
In this paper, we consider there exist two types of fundamental quasihole excitation in the fractional quantum spin Hall state and investigate their topological properties by both Chern-Simons field theory and Berry phase technique. By the…
Drawing on the connection with superconductivity, we give a simple AdS realization of the quantum Hall effect. The theory includes a statistical gauge field with a Chern-Simons term, in analogy with effective field theory models of the QHE.
By allowing the spin degrees of freedom, we present a generalized spin allowed $U(1)\times U(1)$ Chern-Simons theory of fractional quantum Hall effects for odd and even denominator filling factors in single layers. This theory is shown to…
By carefully considering a family of wave functions for Skyrmions in simple quantum Hall states, whose members are labelled by a non-negative integer and which properly generalizes the traditional Laughlin quasiparticle, we argue that the…
We discuss a model of both classical and integer quantum Hall-effect which is based on a semi-classical Schroedinger-Chern-Simons-action, where the Ohm-equations result as equations of motion. The quantization of the classical…
We develop a Fermionic Chern-Simons (CS) theory for the fractional quantum Hall effect in monolayer graphene with SU(4) symmetry, arising from the spin and the valley degrees of freedom, which involves four distinct CS gauge fields. We…
We study the various quantum aspects of the $N=2$ supersymmetric Maxwell Chern-Simons vortex systems. The fermion zero modes around the vortices will give rise the degenerate states of vortices. We analyze the angular momentum of these zero…
It is well known that the Fractional Quantum Hall Effect (FQHE) may be effectively represented by a Chern-Simons theory. In order to incorporate QH Skyrmions, we couple this theory to the topological spin current, and include the Hopf term.…
We derive the effective field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be…
The first part of this paper is a review of the author's work with S. Bahcall which gave an elementary derivation of the Chern Simons description of the Quantum Hall effect for filling fraction $1/n$. The notation has been modernized to…
We investigate fractional quantum Hall effect at finite temperature using a fermion Chern-Simons field theoretical approach. In the absence of impurity scattering, the essential aspects of fractional quantum Hall effect, such as the…
We present an effective Chern-Simons theory for the bulk fully polarized fractional quantum Hall (FQH) hierarchical states constructed as daughters of general states of the Jain series, {\it i. e.} as FQH states of the quasi-particles or…