Related papers: Phase Space Quantum Mechanics as a Landau Level Pr…
We compare the energies of different electron solids, such as bubble crystals with triangular and square symmetry and stripe phases, to those of correlated quantum liquids in partially filled intermediate Landau levels. Multiple transitions…
Quantum mechanical wave functions have phases. These phases either initial or acquired during time evolution usually do not enter the final expressions for observable physical quantities. Nevertheless in many cases the observable physical…
The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and…
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…
The Landau level spectra and the quantum Hall effect of ABA-stacked multilayer graphenes are studied in the effective mass approximation. The low-energy effective mass Hamiltonian may be partially diagonalized into an approximate…
Landau levels have represented a very rich field of research, which has gained widespread attention after their application to quantum Hall effect. In a particular gauge, the holomorphic gauge, they give a physical implementation of…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
Strong correlation brings a rich array of emergent phenomena, as well as a daunting challenge to theoretical physics study. In condensed matter physics, the fractional quantum Hall effect is a prominent example of strong correlation, with…
Suppose a classical electron is confined to move in the $xy$ plane under the influence of a constant magnetic field in the positive $z$ direction. It then traverses a circular orbit with a fixed positive angular momentum $L_z$ with respect…
In this letter, we discuss the recently proposed fractional quantum Hall effect in the absence of Landau levels. It is shown that the parton construction can explain all properties of 1/3 state, including the effective charge of…
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…
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.
The phase-space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including metho ds of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase…
The reduction of the energy gap due to Landau level mixing, characterized by the dimensionless parameter $\lambda = (e^2/\epsilon l_0)/\hbar\omega_c$, has been calculated by variational Monte Carlo for the fractional quantum Hall effect at…
Physics of two-dimensional electron gases under perpendicular magnetic field often displays three distinct stages when increasing the field amplitude: a low field regime with classical magnetotransport, followed at intermediate field by a…
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…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
We compute the effect of Landau-level-mixing on the effective two-body and three-body pseudopotentials for electrons in the lowest and second Landau levels. We find that the resulting effective three-body interaction is attractive in the…
The temperature and scale dependence of resistivities in the standard scaling theory of the integer quantum Hall effect is discussed. It is shown that recent experiments, claiming to observe a discrepancy with the global phase diagram of…
The abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-abelian states emanating from the {\nu} = 5/2 Moore-Read state in the second Landau…