FRACTIONAL STATISTICS ON COMPACT SURFACES

1991 ◽  
Vol 05 (10) ◽  
pp. 675-686 ◽  
Author(s):  
TORBJORN EINARSSON
Keyword(s):  
Statistical Parameter ◽  
Braid Groups ◽  
Simons Theory ◽  
Fractional Statistics ◽  
Quantum Theories ◽  
Component Structure ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Collective Degree ◽  
Rational Multiple

General kinematical restrictions on quantum-theories of N identical anyons have been established by using braid groups. For an orientable compact surface (without boundary) of genus g, the statistical parameter θ is a rational multiple of π, θ=πp/v (p and v mutually prime integers), and the number of components of the wavefunction is (a multiple of) vg. The particle-number is N=rv+1−g (r integer) for spinless (S=0) and N=rv for spinning (S=θ/2π) anyons. The restrictions for spinning anyons are consistent with results for fractional quantum Hall systems, nonlinear O(3) field theory, and Chern-Simons theory. The multi-component structure, which appears for g≥1, reflects an internal collective degree of freedom. A comparison with the multi-component wavefunctions needed to describe systems with fractionally charged quasi-particles yields consistency relations between charge and statistics. Non-orientable surfaces do not allow fractional statistics.

scholarly journals NON-ABELIAN FRACTIONAL QUANTUM HALL STATES AND CHIRAL COSET CONFORMAL FIELD THEORIES

2000 ◽  
Vol 15 (30) ◽  
pp. 4857-4870 ◽  
Author(s):  
D. C. CABRA ◽  
E. FRADKIN ◽  
G. L. ROSSINI ◽  
F. A. SCHAPOSNIK
Keyword(s):  
Quantum Hall ◽  
Field Theories ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Quantum Hall States ◽  
Effective Lagrangian ◽  
Chern Simons

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern–Simons (CS) actions. Our approach exploits the connection between the topological Chern–Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

"MUTUAL FRACTIONAL STATISTICS" AND "RELATIVE ANYONS"

1991 ◽  
Vol 05 (10) ◽  
pp. 1771-1778 ◽  
Author(s):  
Chia-Ren Hu
Keyword(s):  
Quantum Hall ◽  
Ground States ◽  
Two Dimensions ◽  
Statistical Properties ◽  
Phase Factor ◽  
Fractional Statistics ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
General Properties ◽  
Topological Argument

A topological argument similar to that of Leinaas and Myrheim implies that a non-trivial statistical phase factor can also arise from exchanging twice a pair of distinguishable particles in two dimensions. Some general properties of this phase factor are deduced. Wilczek's model for anyons and the Laughlin theory for the quasiparticles in the fractional quantum Hall ground states are examined in light of these properties, and the former is generalized for systems containing many species of anyons. The statistical properties of holons and spinons relative to each other are briefly discussed as an example.

scholarly journals DEFORMED FERMI SURFACE THEORY OF MAGNETO–ACOUSTIC RESPONSE IN MODULATED QUANTUM HALL SYSTEMS NEAR ν=1/2

1999 ◽  
Vol 13 (08) ◽  
pp. 859-868
Author(s):  
NATALIYA A. ZIMBOVSKAYA ◽  
JOSEPH L. BIRMAN
Keyword(s):  
Fermi Surface ◽  
Transport Theory ◽  
Quantum Hall ◽  
Generic Model ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Quantum Hall Regime ◽  
Hall Regime ◽  
Density Modulation ◽  
Dimensional Electron Gas

We develop a magneto-transport theory for the nonlocal response of a two-dimensional electron gas (2DEG) in the Fractional Quantum Hall Regime near ν=1/2 in the presence of a periodic density modulation. We introduce a new generic model of a deformed Composite Fermion–Fermi Surface (CF–FS). Our model permits us to explain recent surface acoustic wave observations of anisotropic anomalies1 in sound velocity and attenuation, such as appearance of peaks and anisotropy, which originate from contributions to the conductivity tensor due to regions of the CF–FS which are flattened by the applied modulation. The calculated magnetic field and wave vector dependence of the CF conductivity, velocity shift and attenuation agree with experiments.

SPIN STRUCTURES IN INHOMOGENEOUS FRACTIONAL QUANTUM HALL SYSTEMS

2004 ◽  
Vol 18 (27n29) ◽  
pp. 3871-3874 ◽  
Author(s):  
KAREL VÝBORNÝ ◽  
DANIELA PFANNKUCHE
Keyword(s):  
Ground State ◽  
Quantum Hall ◽  
Exact Diagonalization ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Spin Structures ◽  
Quantum Hall Systems ◽  
Magnetic Inhomogeneities ◽  
Spin Singlet ◽  
Spin Polarized

Transitions between spin polarized and spin singlet incompressible ground state of quantum Hall systems at filling factor 2/3 are studied by means of exact diagonalization with eight electrons. We observe a stable exactly half–polarized state becoming the absolute ground state around the transition point. This might be a candidate for the anomaly observed during the transition in optical experiments. The state reacts strongly to magnetic inhomogeneities but it prefers stripe–like spin structures to formation of domains.

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