Related papers: Landau quantum systems: an approach based on symme…
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…
We consider a recently proposed network model of the integer quantum Hall (IQH) effect in a weak magnetic field. Using a supersymmetry approach, we reformulate the network model in terms of a superspin ladder. A subsequent analysis of the…
Landau levels in certain models are known to protrude into the zero-field energy gap. These are known as anomalous Landau levels (ALLs). We study whether ALLs can lead to Fermi-surface like quantum oscillation in the absence of a zero-field…
We investigate topological insulating states in both two and three dimensions with the harmonic potential and strong spin-orbit couplings breaking the inversion symmetry. Landau-level like quantizations appear with the full 2D and 3D…
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…
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. Existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external…
We have studied the formation of Hall-qubit (LLL state) in Quantum Hall effect due to the Aharonov-Bhom oscillation of quasiparticles.The spin echo method plays the key role in the topological entanglement of qubits. The proper ratio of…
We show that there is a kind of quantum group symmetry $ sl_{q}(2) $ in the usual Landau problem and it is this quantum group symmetry that governs the degeneracy of Landau levels. We find that under the periodic boundary condition, the…
Characterizing the entanglement of matrix degrees of freedom is essential for understanding the holographic emergence of spacetime. The Quantum Hall Matrix Model is a gauged $U(N)$ matrix quantum mechanics with two matrices whose ground…
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…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
We study the symmetries of non-relativistic systems with an emphasis on applications to the fractional quantum Hall effect. A source for the energy current of a Galilean system is introduced and the non-relativistic diffeomorphism…
We study the Landau level localization and scaling properties of a disordered two-dimensional electron gas in the presence of a strong external magnetic field. The impurities are treated as random distributed scattering centers with…
We investigate the topological insulating states of the $p$-band systems in optical lattices induced by the onsite orbital angular momentum polarization, which exhibit gapless edge modes in the absence of Landau levels. This effect arises…
Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of…
We develop a quantization scheme for the vector potential on globally hyperbolic spacetimes which realizes it as a locally covariant conformal quantum field theory. This result allows us to employ on a large class of backgrounds, which are…
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…
The bootstrap method aims to solve problems by imposing constraints on the space of physical observables, which often follow from physical assumptions such as positivity and symmetry. Here, we employ a bootstrap approach to study…
This article is an expository account aimed at viewing entanglement in finite-dimensional quantum many-body systems as a phenomenon of global geometry. While the mathematics of general quantum states has been studied extensively, this…
The integer quantum Hall effect features a paradigmatic quantum phase transition. Despite decades of work, experimental, numerical, and analytical studies have yet to agree on a unified understanding of the critical behavior. Based on a…