Two-dimensional localization in the presence of random flux and the quantum Hall system at even-denominator filling fractions

1993 ◽  
Vol 48 (15) ◽  
pp. 11095-11106 ◽  
Author(s):  
Vadim Kalmeyer ◽  
Dan Wei ◽  
Daniel P. Arovas ◽  
Shoucheng Zhang
Keyword(s):  
Quantum Hall ◽  
Two Dimensional ◽  
Quantum Hall System

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.

scholarly journals AREA-PRESERVING DIFFEOMORPHISMS, W∞ AND ${\mathcal U}_q [{\rm sl}(2)]$ IN CHERN–SIMONS THEORY AND THE QUANTUM HALL SYSTEM

1994 ◽  
Vol 09 (21) ◽  
pp. 3887-3911 ◽  
Author(s):  
IAN I. KOGAN
Keyword(s):  
Gauge Theory ◽  
Quantum Hall ◽  
Simons Theory ◽  
Two Dimensional ◽  
Canonical Transformations ◽  
Dimensional Phase Space ◽  
Quantum Hall System ◽  
Chern Simons ◽  
Area Preserving ◽  
Chern Simons Theory

We discuss a quantum [Formula: see text] symmetry in the Landau problem, which naturally arises due to the relation between [Formula: see text] and the group of magnetic translations. The latter is connected with W∞ and area-preserving (symplectic) diffeomorphisms which are the canonical transformations in the two-dimensional phase space. We shall discuss the hidden quantum symmetry in a 2 + 1 gauge theory with the Chern–Simons term and in a quantum Hall system, which are both connected with the Landau problem.

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