Related papers: Matrix oscillator and Laughlin Hall states
We illustrate Heisenberg's method of matrix mechanics using the planar quantum rotor example. We show how to find the spectrum of this simple model without the need to use the eigenstates of the system. This then leads us to speculate on…
Here a special case of perturbation in quantum harmonic oscillator is studied. Here we assume the perturbed potential to be a Harmonic Oscillator that has been shifted in the position space.We construct the new creation and annihilation…
The abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-abelian states emanating from the {\nu} = 5/2 Moore-Read state in the second Landau…
We give a brief review of quantum Hall effect in higher dimensions and its relation to fuzzy spaces. For a quantum Hall system, the lowest Landau level dynamics is given by a one-dimensional matrix action whose large $N$ limit produces an…
We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled…
We show that the oscillators on a sphere and pseudosphere are related, by the so-called Bohlin transformation, with the Coulomb systems on the pseudosphere: the even states of an oscillator yields the conventional Coulomb system on…
We study the quantum theory of two-dimensional electrons in a magnetic field and an electric field generated by a homogeneous background. The dynamics separates into a microscopic and macroscopic mode. The latter is a circular Hall current…
In order to obtain a local description of the short distance physics of fractionally quantized Hall states for realistic (e.g. Coulomb) interactions, I propose to view the zeros of the ground state wave function, as seen by an individual…
Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount…
We study lattice wave functions obtained from the SU(2)$_1$ Wess-Zumino-Witten conformal field theory. Following Moore and Read's construction, the Kalmeyer-Laughlin fractional quantum Hall state is defined as a correlation function of…
Recent experimental progress in the creation of synthetic electric and magnetic fields, acting on cold atoms in a two-dimensional lattice, has attracted renewed interest to the problem of a quantum particle in the Hall configuration. The…
We provide a detailed explanation of the formalism necessary to construct matrix product states for non-Abelian quasiholes in fractional quantum Hall model states. Our construction yields an efficient representation of the wave functions…
Making use of the well-known phase space reduction in the lowest Landau level(LLL), we show that the Laughlin wave function for the $\nu = {1\over m}$ case can be obtained exactly as a coherent state representation of an one dimensional…
The present understanding of nonperturbative ground states in the fractional quantum Hall effect is based on effective theories of the Jain "composite fermion" excitations. We review the approach based on matrix variables, i.e. D0 branes,…
We present a quantum field theoretical analysis of a $\nu = 1$ quantum Hall system when the effective Land\'e $g$ factor is small. We clearly demonstrate that the ground state of the system is ferromagnetic. We note that it is the short…
The low-field quantum Hall effect is investigated on a two-dimensional electron system in an AlGaAs/GaAs heterostructure. Magneto-oscillations following the semiclassical Shubnikov-de Haas formula are observed even when the emergence of the…
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…
It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive…
We develop a method to efficiently calculate trial wave functions for quantum Hall systems which involve projection onto the lowest Landau level. The method essentially replaces lowest Landau level projection by projection onto the $M$…
The topological physics of quantum Hall states is efficiently encoded in purely topological quantum field theories of the Chern-Simons type. The reliable inclusion of low-energy dynamical properties in a continuum description however…