Related papers: Phase Separation in the Putative Fractional Quantu…
A series of successive quantizations is considered, starting with the quantization of a non relativistic or relativistic point particle: 1) quantization of a particle's position, 2) quantization of wave function, 3) quantization of wave…
In quantum Hall edge states and in other one-dimensional interacting systems, charge fractionalization can occur due to the fact that an injected charge pulse decomposes into eigenmodes propagating at different velocities. If the original…
We study the excitation spectra and the dynamical structure factor of quantum Hall states in a finite size system through exact diagonalization. Comparison is made between the numerical results so obtained and the analytic results obtained…
We have studied here the newly observed families of fractional quantum Hall states in the framework of Berry phase. It has been shown that this approach embraces in a unified way the whole spectrum of quantum Hall states with their various…
Theory predicts that quasiparticle tunneling between the counter-propagating edges in a fractional quantum Hall state can be used to measure the effective quasiparticle charge e* and dimensionless interaction parameter g, and thereby…
We consider spaces of trial wavefunctions for ground states and edge excitations in the fractional quantum Hall effect that can be obtained in various ways. In one way, functions are obtained by analyzing the entanglement of the ground…
Neural networks (NNs) have great potential in solving the ground state of various many-body problems. However, several key challenges remain to be overcome before NNs can tackle problems and system sizes inaccessible with more established…
The double layer $\nu=2/3$ fractional quantum Hall system is studied using the edge state formalism and finite-size diagonalization subject to periodic boundary conditions. Transitions between three different ground states are observed as…
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…
Direct experimental detection of anyonic exchange statistics in fractional quantum Hall systems by braiding the excitations and measuring the wave-function phase is an enormous challenge. Here, we use a small, noisy quantum computer to…
We apply the stationary phase method developed in (Assier, Shanin \& Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written as a double Fourier transform of an unknown spectral…
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…
The scattering transform is a non-linear signal representation method based on cascaded wavelet transform magnitudes. In this paper we introduce phase scattering, a novel approach where we use phase derivatives in a scattering procedure. We…
We discuss in many details two quantum mechanical models of planar electrons which are very much related to the Fractional Quantum Hall Effect. In particular, we discuss the localization properties of the trial ground states of the models…
In non-interacting systems, disorder can drive a trivial phase into a topological one. However little is known how to construct a fractional quantum Hall ground-state, a paradigmatic topologically ordered state, that exists both in…
Electronic topological phases of matter, characterized by robust boundary states derived from topologically nontrivial bulk states, are pivotal for next-generation electronic devices. However, understanding their complex quantum phases,…
We review understanding of kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected, based on overall composition in a binary liquid or density in a vapor-liquid system, have…
The fractional quantum Hall (FQH) effect refers to the strongly-correlated phenomena and the associated quantum phases of matter realized in a two-dimensional gas of electrons placed in a large perpendicular magnetic field. In such systems,…
The effects of impurity scattering on a general Abelian fractional quantum Hall (FQH) edge state are analyzed within the chiral-Luttinger-liquid model of low-energy edge dynamics. We find that some disordered edges can have several…
Protected edge modes are the cornerstone of topological states of matter. The simplest example is provided by the integer quantum Hall state at Landau level filling unity, which should feature a single chiral mode carrying electronic…