Related papers: Incompressibility Estimates for the Laughlin Phase
States of strongly interacting particles are of fundamental interest in physics, and can produce exotic emergent phenomena and topological structures. We consider here two-dimensional electrons in a magnetic field, and, departing from the…
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…
Motivated by recent advances in quantum gas microscopy, we investigate correlation functions of the current density in many-body Landau Level states, such as the Laughlin state of the fractional quantum Hall effect. For states fully in the…
We present improved wave functions for the ground state, Laughlin quasihole and quasiparticle excitations of the fractional quantum Hall effect. These depend explicitly on the effective strength of Coulomb interaction and reproduce…
We review the theoretical basis and understanding of electronic interactions in graphene Landau levels, in the limit of strong correlations. This limit occurs when inter-Landau-level excitations may be omitted because they belong to a…
A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave…
To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many…
We theoretically examine entanglement in fractional quantum hall states, explicitly taking into account and emphasizing the quasi-two-dimensional nature of experimental quantum Hall systems. In particular, we study the entanglement entropy…
In the context of the fractional quantum Hall effect, we investigate Laughlin's celebrated ansatz for the groud state wave function at fractional filling of the lowest Landau level. Interpreting its normalization in terms of a one component…
On the basis of our previous studies on energy levels and wave functions of single electrons in a strong magnetic field, the energy levels and wave functions of non-interacting electron gas system, electron gas Hall surface density and Hall…
We compare the energies of the Laughlin liquid and a charge density wave in a weak magnetic field for the upper Landau level filling factors $\nu_N = 1/3$ and $1/5$. The charge density wave period has been optimized and was found to be…
We present a novel matrix product representation of the Laughlin and related fractional quantum Hall wavefunctions based on a rigorous version of the correlators of a chiral quantum field theory. This representation enables the quantitative…
The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons…
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…
The analysis of the quantum Hall response of a small system of ultracold bosonic atoms through the variation of its Hall resistivity against the applied gauge magnetic field, provides a powerful method to unmask its strongly correlated…
The robustness of fractional quantum Hall states is measured as the energy gap separating the Laughlin ground-state from excitations. Using thermodynamic approximations for the correlation functions of the Laughlin state and the quasihole…
Interactions among electrons can give rise to striking collective phenomena when the kinetic energy of charge carriers is suppressed. One example is the fractional quantum Hall effect, in which correlations between electrons moving in two…
We quantum mechanically analyze the fractional quantum Hall effect in graphene. This will be done by building the corresponding states in terms of a potential governing the interactions and discussing other issues. More precisely, we…
We study the current and charge distribution of a two dimensional electron gas under strong perpendicular magnetic fields within the linear response regime. We show within a self-consistent screening theory that incompressible strips with…
We present a 6D generalization of the fractional quantum Hall effect involving membranes coupled to a three-form potential in the presence of a large background four-form flux. The low energy physics is governed by a bulk 7D topological…