scholarly journals Explicit mapping between a two-dimensional quantum Hall system and a one-dimensional Luttinger liquid. II. Correlation functions

2007 ◽  
Vol 76 (19) ◽  
Author(s):  
Mats Horsdal ◽  
Jon Magne Leinaas
Keyword(s):  
Correlation Functions ◽  
Quantum Hall ◽  
Luttinger Liquid ◽  
Two Dimensional ◽  
One 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.

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

scholarly journals Relatioship of peaks of correlation functions of amplitude and phase fluctuations with eigen frequencies in oscillation spectrum

2015 ◽  
Vol 1 (3) ◽  
pp. 62-71
Author(s):  
Андрей Поляков ◽  
Andrey Polyakov
Keyword(s):  
Correlation Functions ◽  
Standing Waves ◽  
Cavity Resonator ◽  
Signal Amplitude ◽  
Signal Spectrum ◽  
Universal Relation ◽  
Two Dimensional ◽  
Phase Fluctuations ◽  
One Dimensional ◽  
The Difference

Method of correlation functions of signal amplitude and phase fluctuations (CFAP) is used for processing oscillations in one-dimensional and two-dimensional rectangular cavity resonator models. For all cases, a universal relation, which gives a relationship between the repetition period of peaks on CFAP functions and the difference of adjacent eigenfrequencies in the signal spectrum was obtained. It is shown that for two-dimensional standing wave, this difference can have only two values, each of which corresponds to eigenfrequencies of one-dimensional standing waves. The proposed method allows us to detect all possible one-dimensional standing waves which can occur in the object under study.

QUANTUM HALL EDGE PHYSICS AND ITS ONE-DIMENSIONAL LUTTINGER LIQUID DESCRIPTION

2012 ◽  
Vol 26 (22) ◽  
pp. 1244001 ◽  
Author(s):  
ORION CIFTJA
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Quantum Hall ◽  
Luttinger Liquid ◽  
Edge States ◽  
One Dimensional ◽  
Liquid Model ◽  
Experimental Values ◽  
The One ◽  
The Relationship

We describe the relationship between quantum Hall edge states and the one-dimensional Luttinger liquid model. The Luttinger liquid model originated from studies of one-dimensional Fermi systems, however, it results that many ideas inspired by such a model can find applications to phenomena occurring even in higher dimensions. Quantum Hall systems which essentially are correlated two-dimensional electronic systems in a strong perpendicular magnetic field have an edge. It turns out that the quantum Hall edge states can be described by a one-dimensional Luttinger model. In this work, we give a general background of the quantum Hall and Luttinger liquid physics and then point out the relationship between the quantum Hall edge states and its one-dimensional Luttinger liquid representation. Such a description is very useful given that the Luttinger liquid model has the property that it can be bosonized and solved. The fact that we can introduce a simpler model of noninteracting bosons, even if the quantum Hall edge states of electrons are interacting, allows one to calculate exactly various quantities of interest. One such quantity is the correlation function which, in the asymptotic limit, is predicted to have a power law form. The Luttinger liquid model also suggests that such a power law exponent should have a universal value. A large number of experiments have found the quantum Hall edge states to show behavior consistent with a Luttinger liquid description. However, while a power law dependence of the correlation function has been observed, the experimental values of the exponent appear not to be universal. This discrepancy might be due to various correlation effects between electrons that sometimes are not easy to incorporate within a standard Luttinger liquid model.

scholarly journals One-dimensional flows in the quantum Hall system

1997 ◽  
Vol 500 (1-3) ◽  
pp. 367-378 ◽  
Author(s):  
C.P. Burgess ◽  
C.A. Lütken
Keyword(s):  
Quantum Hall ◽  
One Dimensional ◽  
Quantum Hall System
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