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Quantum Hall (QH) states of 2D single layer optical lattices are examined using Bose-Hubbard model (BHM) in presence of artificial gauge field. We study the QH states of both the homogeneous and inhomogeneous systems. For the homogeneous…
Using the Chalker-Coddington network model as a drastically simplified, but universal model of integer quantum Hall physics, we investigate the plateau-to-insulator transition at strong magnetic field by means of a real-space…
The frictional drag between parallel two-dimensional electron systems has been measured in a regime of strong interlayer correlations. When the bilayer system enters the excitonic quantized Hall state at total Landau level filling factor…
We develop a systematic semiclassical approximation scheme for quantum Hall skyrmions near filling factors $\nu = {1 \over 2n+1}$, which is exact in the long wavelength limit. We construct a coherent state basis for the Hilbert space of…
We report on a study of interaction effects on the polarization of a disordered two-dimensional electron system in a strong magnetic field. Treating the Coulomb interaction within the time-dependent Hartree-Fock approximation we find…
We study the localization properties in the transition from a two-dimensional electron gas at zero magnetic field into an integer quantum Hall (QH) liquid. By carrying out a direct calculation of the localization length for a finite size…
The integer quantum Hall transition (IQHT) is one of the most mysterious members of the family of Anderson transitions. Since the 1980s, the scaling behavior near the IQHT has been vigorously studied in experiments and numerical…
Quantum Hall systems host quasiparticles demonstrating correlated electron physics and non-trivial quantum statistics. Excitonic phases, archetypical for interaction effect, have attracted significant interest in recent years in…
A two-dimensional lattice model for non-interacting fermions in a magnetic field with half a flux quantum per plaquette and $N$ levels per site is considered. This is a model which exhibits the Integer Quantum Hall Effect (IQHE) in the…
We investigate the behavior of disordered interacting electrons in the insulating regime. Our study is based on the quantum Coulomb glass model which is obtained from the classical Coulomb glass by adding hopping matrix elements between…
We analysis the quantum Hall effect exhibited by a system of particles moving in a higher dimensional space. This can be done by considering particles on the Bergman ball {\bb{B}_{\rho}^d} of radius \rho in the presence of an external…
When a fermionic quantum Hall system is projected into the lowest Landau level, there is an exact particle-hole symmetry between filling fractions $\nu$ and $1-\nu$. We investigate whether a similar symmetry can emerge in bosonic quantum…
We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of…
The Pfaffian quantum Hall states, which can be viewed as involving pairing either of spin-polarized electrons or of composite fermions, are generalized by finding the exact ground states of certain Hamiltonians with k+1-body interactions,…
We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal) conductance of a two dimensional electron system placed in a strong perpendicular magnetic field, and subjected to periodic modulations and/or disorder…
We study the localization transition in the integer quantum Hall effect as described by the network model of quantum percolation. Starting from a path integral representation of transport Green's functions for the network model, which…
Electron pairing is a rare phenomenon appearing only in a few unique physical systems; e.g., superconductors and Kondo-correlated quantum dots. Here, we report on an unexpected, but robust, electron "pairing" in the integer quantum Hall…
Two dimensional electronic systems under strong magnetic field form quantum Hall (QH) edge states, which propagate along the boundary of a sample with a dissipationless current. Engineering the pathway of these propagating one-dimensional…
Enhancement of the electron spin polarization in a correlated two-layer two-dimensional electron system at a total Landau level filling factor of one is reported. Using resistively detected nuclear magnetic resonance, we demonstrate that…
We consider models for the plateau transition in the integer quantum Hall effect. Starting from the network model, we construct a mapping to the Dirac Hamiltonian in two dimensions. In the general case, the Dirac Hamiltonian has randomness…