Related papers: Tao-Thouless Revisited
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not…
We consider the fractional quantum Hall effect at the filling $\nu=6/17$, where experiments have observed features of incompressibility in the form of a minimum in the longitudinal resistance. We propose a parton state denoted as…
We numerically study the behavior of spin--$1/2$ fermions on a two-dimensional square lattice subject to a uniform magnetic field, where opposite spins interact via an on-site attractive interaction. Starting from the non-interacting case…
Starting from Laughlin type wave functions with generalized periodic boundary conditions describing the degenerate groundstate of a quantum Hall system we explictly construct $r$ dimensional vector bundles. It turns out that the filling…
We consider the fractional quantum Hall effect (FQHE) at the filling factor $8/17$, where signatures of incompressibility have been observed in the zeroth Landau level of bilayer graphene. We propose an Abelian state described by the…
The 3D state of strongly correlated electrons is proposed, which in the external magnetic field $\vec B$ exhibits the fractional quantum Hall effect, with the zero temperature conductivity tensor $\sigma_{ij} = (e^2/h)(1/m) \sum_k…
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…
In this paper we propose a new assignment for mutual exclusion statistics between quasielectrons and quasiholes in the fractional quantum Hall effect. In addition to providing numerical evidence for this assignment, we show that the…
The topological morphology--order of zeros at the positions of electrons with respect to a specific electron--of Laughlin state at filling fractions $1/m$ ($m$ odd) is homogeneous as every electron feels zeros of order $m$ at the positions…
The fractional quantum Hall effect is a well-known demonstration of strongly correlated topological phases in two dimensions. However, the extension of this phenomenon into a three-dimensional context has yet to be achieved. Recently, the…
Using the parton construction, we build a three-dimensional (3D) multilayer fractional quantum Hall state with average filling \nu = 1/3 per layer that is qualitatively distinct from a stacking of weakly coupled Laughlin states. The state…
From an experimental point of view, quasielectrons and quasiholes play very similar roles in the fractional quantum Hall effect. Nevertheless, the theoretical description of quasielectrons is known to be much harder than the one of…
We argue that a correlated fluid of electrons and holes can exhibit a fractional quantum Hall effect at zero magnetic field analogous to the Laughlin state at filling $1/m$. We introduce a variant of the Laughlin wavefunction for electrons…
In this work, we investigate the nature of the fractional quantum Hall state in the 1/3-filled second Landau level (SLL) at filling factor $\nu=7/3$ (and 8/3 in the presence of the particle-hole symmetry) via exact diagonalization in both…
We study the Laughlin wave function on the cylinder. We find it only describes an incompressible fluid when the two lengths of the cylinder are comparable. As the radius is made smaller at fixed area, we observe a continuous transition to…
We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the nu = 5/2 Moore-Read state, we construct new explicit trial wavefunctions to…
We study the universal long-distance behaviour of the Laughlin state for the fractional quantum Hall effect and the ground state of the Calogero-Sutherland model (one dimensional $1/r^2$ interaction model). In particular, it is shown that…
The energy spectra and wavefunctions of up to 14 interacting quasielectrons (QE's) in the Laughlin nu=1/3 fractional quantum Hall (FQH) state are investigated using exact numerical diagonalization. It is shown that at sufficiently high…
We study an effective Hamiltonian for the standard $\nu=1/3$ fractional quantum Hall system in the thin cylinder regime. We give a complete description of its ground state space in terms of what we call Fragmented Matrix Product States,…
The quasihole states of several paired states, the Pfaffian, Haldane-Rezayi, and 331 states, which under certain conditions may describe electrons at filling factor $\nu=1/2$ or 5/2, are studied, analytically and numerically, in the…