Related papers: Supersymmetry and Localization in the Quantum Hall…
Computer modelling of the integer quantum Hall effect based on self-consistent Hartee-Fock calculations has now reached an astonishing level of maturity. Spatially-resolved studies of the electron density at near macroscopic system sizes of…
We investigate integer and fractional quantum Hall states in quantum point contacts (QPCs) of different geometries, defined in AlGaAs/GaAs heterostructures employing different doping and screening techniques. We find that, even in the…
We study a quantum network percolation model which is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We show dynamical localization for parameters corresponding to edges of Landau…
In two dimensions strongly interacting bosons in a magnetic field can form an integer quantum Hall state. This state has a bulk gap, no fractional charges or topological order in the bulk but nevertheless has quantized Hall transport and…
This thesis explores the application of differential geometric and general relativistic techniques to deepen our understanding of quantum mechanical systems. We focus on three systems, employing these mathematical frameworks to uncover…
The electromagnetic characteristics of the fractional quantum Hall states are studied by formulating an effective vector-field theory that takes into account projection to the exact Landau levels from the beginning. The effective theory is…
We study the localization of particles rotating in a two-dimensional harmonic potential by solving their rotational spectrum using many-particle quantum mechanics and comparing the result to that obtained with quantizing the rigid rotation…
We report on numerical studies of the energy spectrum and the localization properties in the double-layer quantum Hall system at $\nu = 1$. The Coulomb interaction is treated by the Hartree-Fock approximation, and the localization…
We study a system of fermions interacting with a gauge field which can be used to describe either spin liquid or $\nu=1/2$ Quantum Hall state. We propose a generalized model with a dimensionless parameter $N$. We evaluate the properties of…
Ultracold neutral bosons in a rapidly rotating atomic trap have been predicted to exhibit fractional quantum Hall-like states. We describe how the composite fermion theory, used in the description of the fractional quantum Hall effect for…
We reduce the problem of integer quantum Hall transition to a random rotation of an N-dimensional vector by an su(N) algebra, where only N specially selected generators of the algebra are nonzero. The group-theoretical structure revealed in…
The critical behavior of quantum Hall transitions in two-dimensional disordered electronic systems can be described by a class of complicated, non-unitary conformal field theories with logarithmic correlations. The nature and the physical…
A field-theoretic formulation of a planar Hall-electron system with edges is presented and some fundamental aspects of the integer quantum Hall effect are studied with emphasis on clarifying general symmetry-based consequences of…
In a quantum Hall ferromagnet, the spin polarization of the two-dimensional electron system can be dynamically transferred to nuclear spins in its vicinity through the hyperfine interaction. The resulting nuclear field typically acts back…
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative…
Multifractal scaling of critical wave functions at a disorder-driven (Anderson) localization transition is modified near boundaries of a sample. Here this effect is studied for the example of the spin quantum Hall plateau transition using…
The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall…
The quantum efficiency in the transfer of an initial excitation in disordered finite networks, modeled by the $k$-body embedded Gaussian ensembles of random matrices, is studied for bosons and fermions. The influence of the presence or…
The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to explore the underlying physics is to study the wave function that incorporates Fermi-Dirac…
In this paper we propose a new $S$-matrix approach to numerical simulations of network models and apply it to random networks that we proposed in a previous work 10.1103/PhysRevB.95.125414. Random networks are modifications of the…