scholarly journals Noncommutative field theory and composite Fermi liquids in some quantum Hall systems

2020 ◽  
Vol 102 (20) ◽  
Author(s):  
Zhihuan Dong ◽  
T. Senthil
Keyword(s):  
Field Theory ◽  
Quantum Hall ◽  
Fermi Liquids ◽  
Noncommutative Field Theory ◽  
Quantum Hall Systems

scholarly journals Quantum Hall physics = noncommutative field theory

2001 ◽  
Vol 2001 (10) ◽  
pp. 039-039 ◽  
Author(s):  
Simeon Hellerman ◽  
Mark Van Raamsdonk
Keyword(s):  
Field Theory ◽  
Quantum Hall ◽  
Noncommutative Field Theory

scholarly journals Noncommutative field theory description of quantum Hall Skyrmions

2001 ◽  
Vol 64 (8) ◽  
Author(s):  
Bum-Hoon Lee ◽  
Kyungsun Moon ◽  
Chaiho Rim
Keyword(s):  
Field Theory ◽  
Quantum Hall ◽  
Noncommutative Field Theory

scholarly journals A FIELD THEORY FOR THE READ OPERATOR

1996 ◽  
Vol 10 (07) ◽  
pp. 793-803 ◽  
Author(s):  
R. RAJARAMAN ◽  
S. L. SONDHI
Keyword(s):  
Field Theory ◽  
Equations Of Motion ◽  
Quantum Hall ◽  
Mean Field ◽  
Lagrangian Formalism ◽  
Bosonic Field ◽  
Quantum Hall Systems ◽  
Lowest Landau Level ◽  
Bosonic Operator ◽  
Laughlin States

We introduce a new field theory for studying quantum Hall systems. The quantum field is a modified version of the bosonic operator introduced by Read. In contrast to Read's original work we do not work in the lowest Landau level alone, and this leads to a much simpler formalism. We identify an appropriate canonical conjugate field, and write a Hamiltonian that governs the exact dynamics of our bosonic field operators. We describe a Lagrangian formalism, derive the equations of motion for the fields and present a family of mean-field solutions. Finally, we show that these mean field solutions are precisely the Laughlin states. We do not, in this work, address the treatment of fluctuations.

scholarly journals NONCOMMUTATIVE FIELD THEORY AND THE DYNAMICS OF QUANTUM HALL FLUIDS

2002 ◽  
Vol 17 (25) ◽  
pp. 3589-3606 ◽  
Author(s):  
J. L. F. BARBÓN ◽  
A. PAREDES
Keyword(s):  
Field Theory ◽  
Spatial Structure ◽  
Effective Action ◽  
Quantum Hall ◽  
Weak Field ◽  
Density Fluctuations ◽  
Wigner Crystal ◽  
Vertex Operators ◽  
Noncommutative Field Theory ◽  
Chern Simons

We study the spectrum of density fluctuations of fractional Hall fluids in the context of the noncommutative hydrodynamical model of Susskind. We show that, within the weak-field expansion, the leading correction to the noncommutative Chern–Simons Lagrangian (a Maxwell term in the effective action), destroys the incompressibility of the Hall fluid due to strong UV/IR effects at one loop. We speculate on possible relations of this instability with the transition to the Wigner crystal, and conclude that calculations within the weak-field expansion must be carried out with an explicit ultraviolet cutoff at the noncommutativity scale. We point out that the noncommutative dipoles exactly match the spatial structure of the Halperin–Kallin quasiexcitons. Therefore, we propose that the noncommutative formalism must describe accurately the spectrum at very large momenta, provided no weak-field approximations are made. We further conjecture that the noncommutative open Wilson lines are "vertex operators" for the quasiexcitons.

scholarly journals Controllable quantum point junction on the surface of an antiferromagnetic topological insulator

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Nicodemos Varnava ◽  
Justin H. Wilson ◽  
J. H. Pixley ◽  
David Vanderbilt
Keyword(s):  
Topological Insulator ◽  
Information Science ◽  
Domain Walls ◽  
Quantum Hall ◽  
Edge State ◽  
Wave Functions ◽  
Quantum Hall Systems ◽  
Electron Quantum ◽  
Quantum Point ◽  
Higher Temperature

AbstractEngineering and manipulation of unidirectional channels has been achieved in quantum Hall systems, leading to the construction of electron interferometers and proposals for low-power electronics and quantum information science applications. However, to fully control the mixing and interference of edge-state wave functions, one needs stable and tunable junctions. Encouraged by recent material candidates, here we propose to achieve this using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels, one from antiferromagnetic domain walls and the other from single-height steps. Their distinct geometric nature allows them to intersect robustly to form quantum point junctions, which then enables their control by magnetic and electrostatic local probes. We show how the existence of stable and tunable junctions, the intrinsic magnetism and the potential for higher-temperature performance make antiferromagnetic topological insulators a promising platform for electron quantum optics and microelectronic applications.

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