Related papers: Fractionalized anyons in counterflowing Quantum Ha…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
The tunneling rate of fractional charge across a Laughlin state on the cylinder is computed numerically. The decay with strip width Y is fitted to exp[- a (Y/ l)**2/12] where l is the Landau length, and a is approximately 1.0. This rate is…
We employ the exact diagonalization method to analyze the possibility of generating strongly correlated states in two-dimensional clouds of ultracold bosonic atoms which are subjected to a geometric gauge field created by coupling two…
By carefully considering a family of wave functions for Skyrmions in simple quantum Hall states, whose members are labelled by a non-negative integer and which properly generalizes the traditional Laughlin quasiparticle, we argue that the…
We extend the Composite Boson theory to study slightly im-balanced bi-layer Quantum Hall systems. In the global $ U(1) $ symmetry breaking excitonic superfluid side, as the imbalance increases, the system supports continuously changing…
Fractionalized quasiparticles - anyons - bear a special role in present-day physics. At the same time, they display properties of interest both foundational, with quantum numbers that transcend the spin-statistics laws, and applied,…
We provide a brief invitation to the novel understanding of anyonic topological order in fractional quantum (anomalous) Hall systems, via "extraordinary" quantization of effective magnetic flux in Cohomotopy -- following our presentation at…
We present analytic and numerical calculations on the bipartite entanglement entropy in fractional quantum Hall states of the fermionic Laughlin sequence. The partitioning of the system is done both by dividing Landau level orbitals and by…
We review the general strategy of topologically protected quantum information processing based on non-Abelian anyons, in which quantum information is encoded into the fusion channels of pairs of anyons and in fusion paths for multi-anyon…
Current statistics of an antidot in the fractional quantum Hall regime is studied for Laughlin's series. The chiral Luttinger liquid picture of edge states with a renormalized interaction exponent $g$ is adopted. Several peculiar features…
We propose a class of variational wave functions with slow variation in spin and charge density and simple vortex structure at infinity, which properly generalize both the Laughlin quasiparticles and baby Skyrmions. We argue that the spin…
While the values for the fractional charge and fractional statistics coincide for fractional Hall (FQH) states in the Laughlin sequence, they do not for more general FQH states, such as those in the Jain sequence. This mismatch leads to…
Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be…
Entanglement of mixed quantum states can be quantified using the partial transpose and its corresponding entanglement measure, the logarithmic negativity. Recently, the notion of partial transpose has been extended to systems of anyons,…
We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an…
We predict the emergence a state of matter with intertwined ferromagnetism, charge order and topology in fractionally filled moir\'e superlattice bands. Remarkably, these quantum anomalous Hall crystals exhibit a quantized integer Hall…
We present a robust scheme by which fractional quantum Hall states of bosons can be achieved for ultracold atomic gases. We describe a new form of optical flux lattice, suitable for commonly used atomic species with groundstate angular…
The observed fractional quantum Hall (FQH) plateaus follow a recurring hierarchical structure that allows an understanding of complex states based on simpler ones. Condensing the elementary quasiparticles of an Abelian FQH state results in…
Excitons, Coulomb-driven bound states of electrons and holes, are typically composed of integer charges. However, in bilayer systems influenced by charge fractionalization, a more exotic form of interlayer exciton can emerge, where pairing…
Laughlin's Ansatz to explain the fractional Quantum Hall effect is derived by coupling a particle associated with ``exotic'' the two-fold central extension of the planar Galilei group. The reduced system is identical to the one used to…