scholarly journals Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level

1997 ◽  
Vol 11 (22) ◽  
pp. 2621-2660 ◽  
Author(s):  
J. K. Jain ◽  
R. K. Kamilla
Keyword(s):  
Landau Level ◽  
Ground State ◽  
Quantum Hall ◽  
Monte Carlo Study ◽  
Composite Fermions ◽  
Composite Fermion ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Lowest Landau Level ◽  
Standard Manner

Single particle basis functions for composite fermions are obtained from which many-composite fermion states confined to the lowest electronic Landau level can be constructed in the standard manner, i.e. by building Slater determinants. This representation enables a Monte Carlo study of systems containing a large number of composite fermions, yielding new quantitative and qualitative information. The ground state energy and the gaps to charged and neutral excitations are computed for a number of fractional quantum Hall effect (FQHE) states, earlier off-limits to a quantitative investigation. The ground state energies are estimated to be accurate to ~0.1% and the gaps at the level of a few percent. It is also shown that at Landau level fillings smaller than or equal to 1/9 the FQHE is unstable to a spontaneous creation of excitons of composite fermions. In addition, this approach provides new conceptual insight into the structure of the composite fermion wave functions, resolving in the affirmative the question of whether it is possible to motivate the composite fermion theory entirely within the lowest Landau level, without appealing to higher Landau levels.

scholarly journals GEOMETRIC TRANSFORMATIONS AND NCCS THEORY IN THE LOWEST LANDAU LEVEL

2002 ◽  
Vol 16 (25) ◽  
pp. 3725-3736 ◽  
Author(s):  
M. ELIASHVILI ◽  
G. TSITSISHVILI
Keyword(s):  
Landau Level ◽  
Quantum Hall ◽  
Simons Theory ◽  
Composite Fermions ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Geometric Transformations ◽  
Lowest Landau Level ◽  
Chern Simons ◽  
Area Preserving

Chern-Simons type gauge field is generated by the means of singular area preserving transformations in the lowest Landau level of electrons forming fractional quantum Hall state. Dynamics is governed by the system of constraints which correspond to the Gauss law in the non-commutative Chern-Simons gauge theory and to the lowest Landau level condition in the picture of composite fermions. Physically reasonable solution to this constraints corresponds to the Laughlin state. It is argued that the model leads to the non-commutative Chern-Simons theory of the QHE and composite fermions.

W∞-ALGEBRA FOR FERMIONS IN THE LOWEST LANDAU LEVEL

1994 ◽  
Vol 09 (06) ◽  
pp. 549-555 ◽  
Author(s):  
YUN SOO MYUNG
Keyword(s):  
Landau Level ◽  
Ground State ◽  
Condensed Matter ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Fermion Number ◽  
Lowest Landau Level ◽  
Area Preserving

We derive the W∞-algebra directly from the cocycle (translational) transformation of fermions in the lowest Landau level. This happens whenever the translational symmetry is unbroken in the ground state. Under the cocycle transformations, the lowest Landau level condition and fermion number are preserved. In the droplet approximation, the algebra of this system is reduced to the classical w∞-algebra (area-preserving deformations) and is related to condensed matter physics. This describes the edge modes of the fractional quantum Hall effect.

scholarly journals SECOND GENERATION OF COMPOSITE FERMIONS AND THE SELF-SIMILARITY OF THE FRACTIONAL QUANTUM HALL EFFECT

2004 ◽  
Vol 18 (27n29) ◽  
pp. 3549-3552 ◽  
Author(s):  
M. O. GOERBIG ◽  
P. LEDERER ◽  
C. MORAIS SMITH
Keyword(s):  
Second Generation ◽  
Quantum Hall ◽  
Composite Fermions ◽  
Quantum Liquid ◽  
Composite Fermion ◽  
Self Similarity ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Liquid Phases

A recently developed model of interacting composite fermions, is used to investigate different composite-fermion phases. Their interaction potential allows for the formation of both solid and new quantum-liquid phases, which are interpreted in terms of second-generation composite fermions and which may be responsible for the fractional quantum Hall states observed at unusual filling factors, such as ν=4/11. Projection of the composite-fermion dynamics to a single level, involved in the derivation of the Hamiltonian of interacting composite fermions, reveals the underlying self-similarity of the model.

scholarly journals Spectral Function Analysis of Fermi Liquids and of Composite Fermions in A Finite Magnetic Field: Renormalised Gaps

1997 ◽  
Vol 11 (12) ◽  
pp. 1477-1502 ◽  
Author(s):  
S. Curnoe ◽  
P. C. E. Stamp
Keyword(s):  
Landau Level ◽  
Function Analysis ◽  
Level Structure ◽  
Quantum Hall ◽  
Composite Fermions ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Self Energy ◽  
Level Quantization

We consider the self-energy and quasiparticle spectrum, for both electrons interacting with phonons, and composite fermions interacting with gauge fluctuations. In both cases we incorporate the singular structure arising from Landau level quantization in a finite field. This is then used to determine the renormalised gap between the Fermi energy and the first excited states. The electron–phonon problem is treated for both Debye and Einstein phonons. In the case of composite fermions, it is found that the singular Landau level structure strongly affects the renormalised gap in the intermediate coupling regime, which is relevant to experiments on the fractional quantum Hall effect. We compare our findings with measurements of the gap in fractional Hall states with filling fraction ν near ν=1/2.

EXPLANATION OF COMPOSITE FERMION STRUCTURE IN FRACTIONAL QUANTUM HALL SYSTEMS

2012 ◽  
Vol 26 (23) ◽  
pp. 1230011 ◽  
Author(s):  
JANUSZ JACAK ◽  
RYSZARD GONCZAREK ◽  
LUCJAN JACAK ◽  
IRENEUSZ JÓŹWIAK
Keyword(s):  
Quantum Hall ◽  
High Mobility ◽  
Flat Band ◽  
Composite Fermions ◽  
Composite Fermion ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Flux Tubes ◽  
Quantum Hall Systems ◽  
Developing Area

The topological explanation of the origin of Laughlin correlations in 2D charged systems under strong magnetic fields is formulated. Formal, self-consistent mathematical model of originally identified cyclotron braid subgroups is given in order to fully describe fundamentals of fractional quantum Hall effect, retrieve Laughlin correlations and point physical conditions which stand behind mysterious composite fermion structure. The new complete implementation of composite fermion basing on the first principles, without involving any artificial constructions (with flux-tubes or vortices) supply an explanation of previous models of composite fermions. Presented approach can lead to some corrections of numerical results in energy minimizations made within the traditional formulation of composite fermion model. Authors also identify the relations of FQHE in cyclotron braid terms within newly developing area of topological insulators and optical lattices. The prerequisites needed for formation of the fractional state are identified beyond the traditionally assumed factors, like the flat band condition and the interaction presence. The role of high mobility of carriers is highlighted in agreement with the experimental observations. Description, in terms of cyclotron braid subgroups, of the nature of yet unexplained novel experiments in Hall 2D systems including graphene is provided as well.

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