Lowest-Landau-level constraint, Goldstone mode, and Josephson effect in a double-layer quantum Hall system

1993 ◽  
Vol 48 (20) ◽  
pp. 15189-15197 ◽  
Author(s):  
Z. F. Ezawa ◽  
A. Iwazaki
Keyword(s):  
Landau Level ◽  
Double Layer ◽  
Josephson Effect ◽  
Quantum Hall ◽  
Goldstone Mode ◽  
Lowest Landau Level ◽  
Quantum Hall System

scholarly journals THE HYDRODYNAMICAL LIMIT OF QUANTUM HALL SYSTEM

2001 ◽  
Vol 15 (19n20) ◽  
pp. 2771-2781 ◽  
Author(s):  
D. SREEDHAR BABU ◽  
R. SHANKAR ◽  
M. SIVAKUMAR
Keyword(s):  
Landau Level ◽  
Small Amplitude ◽  
Quantum Hall ◽  
Collective Excitations ◽  
Current Form ◽  
Long Wavelength ◽  
Lowest Landau Level ◽  
Hydrodynamical Limit ◽  
Quantum Hall System ◽  
A Current

We study the current algebra of FQHE systems in the hydrodynamical limit of small amplitude, long-wavelength fluctuations. We show that the algebra simplifies considerably in this limit. The Hamiltonian is expressed in a current–current form and the operators creating inter-Landau level and lowest Landau level collective excitations are identified.

scholarly journals On the Constraint Equation for the Lowest Landau Level in Fractional Quantum Hall System

1991 ◽  
Vol 05 (10) ◽  
pp. 1715-1724 ◽  
Author(s):  
Dong-Ning Sheng ◽  
Zhao-Bin Su ◽  
B. Sakita
Keyword(s):  
Field Theory ◽  
Landau Level ◽  
Quantum Hall ◽  
Constraint Equation ◽  
Wave Functions ◽  
Generic Properties ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Lowest Landau Level ◽  
Quantum Hall System

In the framework of collective field theory, We apply the Chern-Simon field theory treatment to the constraint equation for the lowest Landau level to investigate the generic properties for the quasi-particles of the FQH system. It shows a transparent connection to the Laughlin's wave functions. If we take an average over the wave functional for the constraint equation, the resulted equation can be interpreted as the vortex equation for the fractionally charged quasi-particles. Introducing a generalized ρ (density)-ϑ (phase) transformation, not only the fractional statistics and the hierarchy scheme can be drawn from the constraint equation, it also gives rise an interesting picture that vortices condense as a Halperin like wave fuction on a Laughlin like background condensate of ν=1/m.

W INFINITE SYMMETRIES IN THE HIERARCHICAL QUASIPARTICLE STATES (LOWEST LANDAU LEVEL STATES) OF THE FRACTIONAL QUANTUM HALL SYSTEMS

1995 ◽  
Vol 09 (02) ◽  
pp. 195-219
Author(s):  
YI-XIN CHEN ◽  
ZHONG-SHUI MA ◽  
ZHAO-BIN SU
Keyword(s):  
Landau Level ◽  
Quantum Hall ◽  
Symmetric Algebra ◽  
Operator Product ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Symmetric Algebras ◽  
Lowest Landau Level ◽  
Quantum Hall System ◽  
Infinite Symmetries

We investigate the W infinite symmetries in the theory of general fractional quantum Hall effects by using the lowest Landau level constraint approach. We find that there does exist a W infinite symmetric algebra for the fractional quantum Hall system with all the quasiparticles being restricted to the lowest Landau level. The corresponding generators can be used to generate the new degenerate wavefunctions of the lowest Landau level states by means of Laughlin and Halperin wavefunctions. Meanwhile, we find there still exists another W infinite symmetric algebra in the system, whose generators are used to generate the degenerate wavefunctions of the lowest Landau level for the anti-quasiparticles. We conclude that the FQH system can effectively be described by quasiparticle features or anti-quasiparticle features. We also show that the local part of the W infinite symmetric algebras is the magnetic translation operator of the general fractional quantum Hall system. We finally construct the operators of the single mode wave density excitations in the system and discuss their operator product relations.

Superfluidity of the Lattice Anyon Gas

1989 ◽  
Vol 03 (12) ◽  
pp. 1965-1995 ◽  
Author(s):  
Eduardo Fradkin
Keyword(s):  
Quantum Hall ◽  
Goldstone Mode ◽  
Two Dimensional ◽  
Hall Conductance ◽  
Dimensional Lattice ◽  
Quantum Hall Systems ◽  
Wigner Transformation ◽  
Topological Invariance ◽  
Quantum Hall System ◽  
Chern Simons

I consider a gas of “free” anyons with statistical paremeter δ on a two dimensional lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on a lattice coupled to a Chern-Simons gauge theory with coupling [Formula: see text]. I show that if [Formula: see text] and the density [Formula: see text], with r and q integers, the system is a superfluid. If q is even and the system is half filled the state may be either a superfluid or a Quantum Hall System depending on the dynamics. Similar conclusions apply for other values of ρ and δ. The dynamical stability of the Fetter-Hanna-Laughlin goldstone mode is insured by the topological invariance of the quantized Hall conductance of the fermion problem. This leads to the conclusion that anyon gases are generally superfluids or quantum Hall systems.

Dynamics of the inter-Landau-level magnetoplasmon coherence in a quantum Hall system

2005 ◽  
Author(s):  
K.M. Dani ◽  
J. Tignon ◽  
M. Breit ◽  
D.S. Chemla ◽  
E.G. Kavousanaki ◽  
...  
Keyword(s):  
Landau Level ◽  
Quantum Hall ◽  
Quantum Hall System
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