Related papers: Anisotropic Quantum Hall Matrix Model
The compressibility of a two-dimensional electron system with spin in a spatially correlated random potential and a quantizing magnetic field is investigated. Electron-electron interaction is treated with the Hartree-Fock method. Numerical…
In this Chapter, we give a brief review of the state of the art of theoretical and experimental studies of synthetic magnetic fields and quantum Hall effects in ultracold atomic gases. We focus on integer, spin, and fractional Hall effects,…
We investigate fast rotating quasi-two-dimensional dipolar Fermi gases in the quantum Hall regime. By tuning the direction of the dipole moments with respect to the z-axis, the dipole-dipole interaction becomes anisotropic in the $x$-$y$…
Motivated by recent experimental attempts to detect the Hofstadter butterfly, we numerically calculate the Hall conductivity in a modulated two-dimensional electron system with disorder in the quantum Hall regime. We identify the critical…
We consider stripe formation in quantum Hall systems at integer filling factors. We use Hartree-Fock calculations to obtain the phase diagram of bilayer quantum Hall systems at $\nu=4n+1$ in a tilted magnetic field. We derive and analyze an…
We study the quantum-mechanical bootstrap as it applies to the bound states of several central potentials in three dimensions. As part of this effort, we show how the bootstrap approach may be applied to ``non-algebraic'' potentials, such…
g-factor tuning of electrons in quantum dots is studied as function of in-plane and perpendicular magnetic fields for different confinements. Rashba and Dresselhaus effects are considered, and comparison is made between wide- and narrow-gap…
The field induced quantum critical properties of the three dimensional spin-1/2 anisotropic antiferromagnetic Heisenberg model has been studied. We have investigated the quantum phase transition between the spiral order and field induced…
A fractional quantum Hall (FQH) system with broken rotational symmetry exploits its geometric degree of freedom to minimize its ground state energy. The mass anisotropy of bare particles interacting isotropically is partially inherited by…
We study the physics of $\nu=1/2$ bosonic fractional quantum Hall droplets confined in a ring-shaped region delimited by two concentric cylindrically symmetric hard-wall potentials. Trial wave functions based on an extension of the Jack…
We derive semiclassical ground state solutions that correspond to the quantum Hall states earlier found in the Maxwell-Chern-Simons matrix theory. They realize the Jain composite-fermion construction and their density is piecewise constant…
It was recently pointed out that topological liquid phases arising in the fractional quantum Hall effect (FQHE) are not required to be rotationally invariant, as most variational wavefunctions proposed to date have been. Instead, they…
In this work a method based on a topological invariance of rational tangles commonly used in knot theory determines filling factors in the fractional quantum Hall effect. The main sustain for this hypothesis are the Schubert's theorems…
We study the dynamics of a quantum or classical particle in a two-dimensional rotating anisotropic harmonic potential. By a sequence of symplectic transformations for constant rotation velocity we find uncoupled normal generalized…
The mechanical effects in finite two-dimensional electron systems (quantum dots or droplets) in a strong perpendicular magnetic field are studied. It is shown that, due to asymmetry of the cyclotron dynamics, an additional in-plane electric…
A model system is considered where two dimensional electrons are confined by a harmonic potential in one direction, and are free in the other direction. Ground state in strong magnetic fields is investigated through numerical…
We develop a matrix model to describe bilayered quantum Hall fluids for a series of filling factors. Considering two coupling layers, and starting from a corresponding action, we construct its vacuum configuration at \nu=q_iK_{ij}^{-1}q_j,…
We revisit the quantum theory of a massive, minimally coupled scalar field, propagating on the Planck-era isotropic cosmological quantum spacetime which transitions to a classical spacetime in later times. The quantum effects modify the…
This work deals with the effects of an anharmonic trap on an interacting two-boson system in one dimension. Our primary focus is on the role of the induced coupling between the center of mass and the relative motion as both anharmonicity…
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…