Related papers: Duality and anyonic excitations
We have tested Haldane's ``fractional-Pauli-principle'' description of excitations around the $\nu = 1/3$ state in the FQHE, using exact results for small systems of electrons. We find that Haldane's prediction $\beta = \pm 1/m$ for…
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…
A two-dimensional electron system exposed to a strong magnetic field produces a plethora of strongly interacting fractional quantum Hall (FQH) states, the complex topological orders of which are revealed through exotic emergent particles,…
It is commonly believed that light cannot couple to the collective excitations of the fractional quantum Hall effect (FQHE). This assumption relies on Kohn's theorem that states that electron-electron interactions decouple from homogeneous…
The Heisenberg double of a Hopf algebra may be regarded as a quantum analogue of the cotangent bundle of a Lie group. Quantum duality principle describes relations between a Hopf algebra, its dual, and their Heisenberg double in a way which…
We explore the consequences of introducing a complex conductivity into the quantum Hall effect. This leads naturally to an action of the modular group on the upper-half complex conductivity plane. Assuming that the action of a certain…
We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in $(2+1)$ dimensions (QED$_3$) with $N = 1$ fermion flavors. The duality proceeds via an exact, non-local mapping from electrons to dual…
We use Pseudo Quantum Electrodynamics to study massive (2+1)D Dirac systems interacting electromagnetically via a U(1) gauge field in (3+1)D. It was recently found in Ref. [1], that an interaction-induced Quantum Hall Effect (QHE) and…
We study Kitaev's quantum double model for arbitrary finite gauge group in infinite volume, using an operator-algebraic approach. The quantum double model hosts anyonic excitations which can be identified with equivalence classes of…
A topological interpretation of the electron--electron interaction under FQHE conditions gives rise to the existence of some kind of composite fermions. The interaction term is similar to the Coulomb interaction and produces punctures in…
For any causal nonlinear electrodynamics theory that is "self-dual" (electromagnetic $U(1)$-duality invariant), the Legendre-dual pair of Lagrangian and Hamiltonian densities $\{\mathcal{L},\mathcal{H}\}$ are constructed from functions…
The fractional quantum Hall effect, where plateaus in the Hall resistance at values of coexist with zeros in the longitudinal resistance, results from electron correlations in two dimensions under a strong magnetic field. Current flows…
The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary…
The fractional quantum Hall (FQH) effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most FQH studies have focused on the lowest Landau level (LL), whose fractional states are…
Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving…
The fractional quantum Hall effect (FQHE) is a canonical example of a topological phase in a correlated 2D electron gas under strong magnetic field. While electric currents propagate as chiral downstream edge modes, chargeless upstream…
The fractional quantum Hall (FQH) effect is reported in a high mobility CdTe quantum well at mK temperatures. Fully-developed FQH states are observed at filling factor 4/3 and 5/3 and are found to be both spin-polarized ground state for…
We present an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For…
Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semi-circle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of…
We find that in "two-photon"-like processes in the scalar $\varphi^3_E$ model and also in hadron-pair production arising from the collisions of a real (transversely polarized) and a highly virtual, longitudinally polarized, photon in QCD,…