Related papers: A simple view on the quantum Hall system
We study a quantum particle propagating through a ``quantum mechanically chaotic'' background, described by parametric random matrices with only short range spatial correlations. The particle is found to exhibit turbulent-like diffusion…
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the…
We show how the modular symmetries that have been found to be consistent with most available scaling data from quantum Hall systems, derive from a rigid family of algebraic curves of the elliptic type. The complicated special functions…
Experiments on a nearly spin degenerate two-dimensional electron system reveals unusual hysteretic and relaxational transport in the fractional quantum Hall effect regime. The transition between the spin-polarized (with fill fraction $\nu =…
Any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. This allows to decompose a quantum system into subsystems. We propose a simple tractable model for a constructive study of…
Topological quantum states have been proposed and investigated on two-dimensional flat surfaces or lattices with different geometries like the plane, cylinder and torus. Here, we study quantum anomalous Hall (QAH) or Chern insulator (CI)…
The Halperin $(m,m',n)$ bilayer quantum Hall states are studied on thin cylinders. In this limit, charge density wave patterns emerge that are characteristic of the underlying quantum Hall state. The general patterns are worked out from a…
This work deals with lump-like structures in models described by a single real scalar field in two-dimensional spacetime. We start with a model that supports lump-like configurations and use the deformation procedure to construct scalar…
We propose a new formula that extracts the quantum Hall conductance from a single (2+1)D gapped wavefunction. The formula applies to general many-body systems that conserve particle number, and is based on the concept of modular flow: i.e.,…
During the past decades, theorists have been studying quantum mechanical systems that are believed to describe black holes. We review one of the simplest examples. It involves a collection of interacting oscillators and Majorana fermions.…
Double layer quantum Hall systems have interesting properties associated with interlayer correlations. At $\nu =1/m$ where $m$ is an odd integer they exhibit spontaneous symmetry breaking equivalent to that of spin $1/2$ easy-plane…
We describe a quantum particle constrained on a catenoid, employing an effective description of quantum mechanics based on expected values of observables and quantum dispersions. We obtain semiclassical trajectories for particles,…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…
Previously we have proposed that in certain relativistic quantum field theories knotlike configurations may appear as stable solitons. Here we present a detailed investigation of the simplest knotted soliton, the torus-shaped unknot.
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…
We explore the characteristics of equilibrium tunneling of electrons from a 3D electrode into a high mobility 2D electron system. For most 2D Landau level filling factors, we find that tunneling can be characterized by a single,…
We study the quantum Hall plateau transition on rectangular tori. As the aspect ratio of the torus is increased, the two-dimensional critical behavior, characterized by a subthermodynamic number of topological states in a vanishing energy…
We present a simple classification of the different liquid and solid phases of quantum Hall systems in the limit where the Coulomb interaction between the electrons is significant, i.e. away from integral filling factors. This…
Continuous transitions between states with the {\em same} symmetry but different topological orders are studied. Clean quantum Hall (QH) liquids with neutral quasiparticles are shown to have such transitions. For clean bilayer (nnm) states,…
The extraordinary success in laser cooling, trapping, and coherent manipulation of atoms has energized the efforts in extending this exquisite control to molecules. Not only are molecules ubiquitous in nature, but the control of their…