Phase Boundaries between Quantum Hall Metaland Hall Insulator in Si-MOSFET's and Many-Body Enhancement of Valley- and Zeeman-Splitting

The edge states of the quantum Hall effect carry representations of chiral current algebras and their associated groups. In the simplest case of a single filled Landau level, I demonstrate explicitly how the group action affects the many-body states, and why the Kac-Peterson cocycle appears in the group multiplication law. I show how these representations may be used to construct vertex operators which create localised edge excitations, and indicate how they are related to the bulk quasi-particles.

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Simulation of the many-body dynamical quantum Hall effect in an optical lattice

Quantum Information Processing ◽

10.1007/s11128-016-1252-9 ◽

2016 ◽

Vol 15 (5) ◽

pp. 1909-1920 ◽

Cited By ~ 1

Author(s):

Dan-Wei Zhang ◽

Xu-Chen Yang

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Optical Lattice ◽

Quantum Hall ◽

Many Body ◽

The Many

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Substratum Interpretation of the Quark-Lepton Symmetries in the Planck Aether Model of a Unified Field Theory

Zeitschrift für Naturforschung A ◽

10.1515/zna-1991-0612 ◽

1991 ◽

Vol 46 (6) ◽

pp. 551-559 ◽

Cited By ~ 4

Author(s):

F. Winterberg

Keyword(s):

Field Theory ◽

Vector Boson ◽

Quantum Hall ◽

Zero Point ◽

Unified Field Theory ◽

Many Body ◽

Fractional Quantum Hall ◽

Unified Field ◽

A Value ◽

The Many

Abstract An attempt is made to explain the observed quark-lepton symmetries in the framework of the recently proposed Planck aether model of a unfied field theory. If the many body lepton wave function can rearrange itself into a vortex-substructure, very much as it has been observed in the fractional quantum Hall effect, all the symmetries can be understood by the quantum numbers of these vortices and their interactions, and all fermions as permitted combinations of those vortices, including the correct number of force-transmitting bosons. The proposed model can also give a value for the mass of the intermediate vector boson. All charges are explained by the quantum mechanical zero point fluctuations of the Planck masses making up the Planck aether

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Non-Hermitian fractional quantum Hall states

Scientific Reports ◽

10.1038/s41598-019-53253-8 ◽

2019 ◽

Vol 9 (1) ◽

Cited By ~ 26

Author(s):

Tsuneya Yoshida ◽

Koji Kudo ◽

Yasuhiro Hatsugai

Keyword(s):

Ground State ◽

Cold Atoms ◽

Quantum Hall ◽

Quantum Zeno Effect ◽

Many Body ◽

Fractional Quantum ◽

Fractional Quantum Hall ◽

Zeno Effect ◽

Quantum Hall States ◽

The Many

AbstractWe demonstrate the emergence of a topological ordered phase for non-Hermitian systems. Specifically, we elucidate that systems with non-Hermitian two-body interactions show a fractional quantum Hall (FQH) state. The non-Hermitian Hamiltonian is considered to be relevant to cold atoms with dissipation. We conclude the emergence of the non-Hermitian FQH state by the presence of the topological degeneracy and by the many-body Chern number for the ground state multiplet showing Ctot = 1. The robust topological degeneracy against non-Hermiticity arises from the manybody translational symmetry. Furthermore, we discover that the FQH state emerges without any repulsive interactions, which is attributed to a phenomenon reminiscent of the continuous quantum Zeno effect.

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WILSON LOOPS AND NON-ABELIAN STATISTICS IN THE QUANTUM HALL EFFECT

International Journal of Modern Physics B ◽

10.1142/s0217979292002280 ◽

1992 ◽

Vol 06 (17) ◽

pp. 2875-2891

Author(s):

MICHAEL STONE

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Quantum Hall ◽

Conductivity Tensor ◽

Hall Conductivity ◽

Wilson Loops ◽

Many Body ◽

Quantum Numbers ◽

The Many ◽

Chern Simons

There is a topological connection between the boundary excitations of a quantum Hall fluid and the quantum numbers of its vortex-like bulk quasi-particles. I use this connection to examine the group properties of vortex excitations in a generalized quantum Hall fluid, and show how the vortex trajectories become Wilson lines interacting via Chern-Simons fields. As a result, I argue that non-abelian statistics, if they exist, should be independent of the detailed properties of the many-body wavefunction and will depend only on the bulk Hall conductivity tensor.

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Electron-hole asymmetric integer and fractional quantum Hall effect in bilayer graphene

Science ◽

10.1126/science.1250270 ◽

2014 ◽

Vol 345 (6192) ◽

pp. 55-57 ◽

Cited By ~ 67

Author(s):

A. Kou ◽

B. E. Feldman ◽

A. J. Levin ◽

B. I. Halperin ◽

K. Watanabe ◽

...

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Quantum Hall ◽

Bilayer Graphene ◽

Fractional Quantum Hall Effect ◽

Many Body ◽

Electron Hole ◽

Fractional Quantum ◽

Fractional Quantum Hall ◽

Lowest Landau Level

The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The distinct combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce an unusual and tunable sequence of FQH states. Here, we present local electronic compressibility measurements of the FQH effect in the lowest Landau level of bilayer graphene. We observe incompressible FQH states at filling factors ν = 2p + 2/3, with hints of additional states appearing at ν = 2p + 3/5, where p = –2, –1, 0, and 1. This sequence breaks particle-hole symmetry and obeys a ν → ν + 2 symmetry, which highlights the importance of the orbital degeneracy for many-body states in bilayer graphene.

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