Fractional statistics of Laughlin quasiparticles in quantum antidots

2005 ◽  
Vol 71 (15) ◽  
Author(s):  
V. J. Goldman ◽  
Jun Liu ◽  
A. Zaslavsky
Keyword(s):  
Fractional Statistics

"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.

GENERAL COVARIANCE, TOPOLOGICAL QUANTUM FIELD THEORIES AND FRACTIONAL STATISTICS

1992 ◽  
Vol 07 (02) ◽  
pp. 209-234 ◽  
Author(s):  
J. GAMBOA
Keyword(s):  
Hamiltonian Formalism ◽  
Field Theories ◽  
General Covariance ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Fractional Statistics ◽  
Multiply Connected ◽  
Topological Quantum ◽  
Gauge Fixing ◽  
Topological Quantum Field Theories

Topological quantum field theories and fractional statistics are both defined in multiply connected manifolds. We study the relationship between both theories in 2 + 1 dimensions and we show that, due to the multiply-connected character of the manifold, the propagator for any quantum (field) theory always contains a first order pole that can be identified with a physical excitation with fractional spin. The article starts by reviewing the definition of general covariance in the Hamiltonian formalism, the gauge-fixing problem and the quantization following the lines of Batalin, Fradkin and Vilkovisky. The BRST–BFV quantization is reviewed in order to understand the topological approach proposed here.

THE PAULI TERM AS A GENERATOR OF FRACTIONAL SPIN

2011 ◽  
Vol 26 (19) ◽  
pp. 1427-1432
Author(s):  
J. S. N. FURTADO ◽  
F. A. S. NOBRE
Keyword(s):  
Fractional Statistics ◽  
Fractional Spin ◽  
Chern Simons ◽  
Matter Fields

In this work, we show that contrary to what is commonly accepted by the community, the Chern–Simons term is not essential to fractional statistics. A Lagrangian whose dynamics is governed only by the Pauli term coupled to matter fields leads to the fractional spin. Despite its simplicity, development of this Lagrangian gives rise to essentially the same terms that appear in Chern–Simons models, such as those reported by Nobre and Almeida.13,8,9

scholarly journals Topological Order: From Long-Range Entangled Quantum Matter to a Unified Origin of Light and Electrons

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Xiao-Gang Wen
Keyword(s):  
Symmetry Breaking ◽  
Long Range ◽  
Topological Order ◽  
Fractional Statistics ◽  
Microscopical Level ◽  
Macroscopic Level ◽  
Emergent Phenomena ◽  
Quantum Matter ◽  
Ordered Phases ◽  
Zero Viscosity

We review the progress in the last 20–30 years, during which we discovered that there are many new phases of matter that are beyond the traditional Landau symmetry breaking theory. We discuss new “topological” phenomena, such as topological degeneracy that reveals the existence of those new phases—topologically ordered phases. Just like zero viscosity defines the superfluid order, the new “topological” phenomena define the topological order at macroscopic level. More recently, we found that at the microscopical level, topological order is due to long-range quantum entanglements. Long-range quantum entanglements lead to many amazing emergent phenomena, such as fractional charges and fractional statistics. Long-range quantum entanglements can even provide a unified origin of light and electrons; light is a fluctuation of long-range entanglements, and electrons are defects in long-range entanglements.

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