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.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory

2002 ◽  
Vol 2002 (01) ◽  
pp. 002-002 ◽  
Author(s):  
Alexander Gorsky ◽  
Ian I Kogan ◽  
Chris Korthals-Altes
Keyword(s):  
Quantum Hall ◽  
Simons Theory ◽  
Quantum Hall System ◽  
Chern Simons ◽  
Chern Simons Theory

Topological invariance of the Hall conductance and quantization

2015 ◽  
Vol 29 (24) ◽  
pp. 1550135
Author(s):  
Paul Bracken
Keyword(s):  
Chern Class ◽  
Fiber Bundle ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Hall Conductance ◽  
Integer Multiple ◽  
Principal Fiber Bundle ◽  
Topological Invariance ◽  
First Chern Class

It is shown that the Kubo equation for the Hall conductance can be expressed as an integral which implies quantization of the Hall conductance. The integral can be interpreted as the first Chern class of a [Formula: see text] principal fiber bundle on a two-dimensional torus. This accounts for the conductance given as an integer multiple of [Formula: see text]. The formalism can be extended to deduce the fractional conductivity as well.

scholarly journals Non-commutative Chern–Simons for the quantum Hall system and duality

2002 ◽  
Vol 642 (3) ◽  
pp. 483-500 ◽  
Author(s):  
Eduardo Fradkin ◽  
Vishnu Jejjala ◽  
Robert G. Leigh
Keyword(s):  
Quantum Hall ◽  
Quantum Hall System ◽  
Chern Simons

Two-dimensional polaron mass in ZnO quantum Hall systems

2010 ◽  
Vol 7 (6) ◽  
pp. 1599-1601 ◽  
Author(s):  
Y. Imanaka ◽  
T. Takamasu ◽  
H. Tampo ◽  
H. Shibata ◽  
S. Niki
Keyword(s):  
Quantum Hall ◽  
Two Dimensional ◽  
Quantum Hall Systems

scholarly journals JOSEPHSON EFFECT AND ASSOCIATED PHENOMENA IN DOUBLE-LAYER QUANTUM HALL SYSTEMS

1994 ◽  
Vol 08 (16) ◽  
pp. 2111-2155 ◽  
Author(s):  
Z.F. EZAWA ◽  
A. IWAZAKI
Keyword(s):  
Double Layer ◽  
Josephson Effect ◽  
Cooper Pair ◽  
Quantum Hall ◽  
Meissner Effect ◽  
Plasmon Excitation ◽  
Josephson Tunneling ◽  
Quantum Hall Systems ◽  
System A ◽  
Chern Simons

In certain double-layer quantum Hall systems we show the existence of Josephson phenomena such as the Josephson effect, the Meissner effect and the Anderson plasmon excitation. The distinctive feature is that the unit of the charge associated with the Josephson tunneling is e of the single electron and not 2e of the Cooper pair. We develop a theory of these Josephson phenomena by using the Chern-Simons formulation of the planar electrons. We explain our results by using the pseudospin language. Furthermore, we point out that Anderson plasmon excitations may already have been observed by a recent experiment on a double-layer quantum Hall system. A microwave experiment without attaching external leads is proposed for a direct observation of plasmon excitations.

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