Related papers: The quantum Hall hierarchy in spherical geometry
Since the ground-breaking discovery of the quantum Hall effect, half-quantized quantum Hall plateaus have been some of the most studied and sought-after states. Their importance stems not only from the fact that they transcend the composite…
We consider the geometric part of the effective action for Fractional Quantum Hall Effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to the obtain correct gravitational linear…
It is widely accepted that topological quantities are useful to describe quantum liquids in low dimensions. The (spin) Hall conductances are typical examples. They are expressed by the Chern numbers, which are topological invariants given…
The higher dimensional quantum Hall liquid constructed recently supports stable topological membrane excitations. Here we introduce a microscopic interacting Hamiltonian and present its exact ground state wave function. We show that this…
We have pursued in the literature a fractal-like structure for the fractional quantum Halll effect-FQHE which consider the Hausdorff dimension associated with the quantum mechanics paths and the spin of the particles or quasiparticles…
The recently introduced classification of two-dimensional insulators in terms of topological crystalline invariants has been applied so far to "obstructed" atomic insulators characterized by a mismatch between the centers of the electronic…
We develop a microscopic formalism to study the fractional quantum Hall plateaus at filling factors $\nu $ away from $1/2\beta$ $\beta$ an integer. The theory is in terms of quasiparticles which carry a charge $e^{\ast}$ equal to…
It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
We demonstrate that formulating the composite-fermion theory of the fractional quantum Hall (FQH) effect in terms of quaternions greatly expands its reach and opens the door into many interesting issues that were previously beyond the reach…
We establish a variational principle for properly mapping a fractional quantum Hall (FQH) state to a fractional Chern insulator (FCI). We find that the mapping has a gauge freedom which could generate a class of FCI ground state wave…
Topological states of quantum matter have inspired both fascinating physics findings and exciting opportunities for applications. Due to the over-complicated structure of, as well as interactions between, real materials, a faithful quantum…
Study of the ground-state electronic spin-polarization can permit discovery and identification of novel correlated phases in the quantum Hall (QH) system. It can thus determine the potential usefulness of QH states for quantum computing.…
We show the explicit connection between two distinct and complementary approaches to the fractional quantum Hall system (FQHS): the quantum wires formalism and the topological low-energy effective description given in terms of an Abelian…
Composite fermions (CFs) of the fractional quantum Hall effect are described as spherical products of electron and vortex spinors, built from underlying L=1/2 ladder operators aligned so that the spinor angular momenta Le and Lv are…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
It is demonstrated that all observed fractions at moderate Landau level fillings in the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
By explicitly identifying a basis valid for any number of electrons, we demonstrate that simple multi-quasihole wavefunctions for the $\nu=1/2$ Pfaffian paired Hall state exhibit an exponential degeneracy at fixed positions. Indeed, we…
We investigate theoretically the fractional quantum Hall effect at half-filling in the lowest Landau level observed in asymmetric wide quantum wells. The asymmetry can be achieved by a potential bias applied between the two sides of the…
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…
The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both…