scholarly journals Edge states for the Kalmeyer-Laughlin wave function

2015 ◽  
Vol 92 (24) ◽  
Author(s):  
Benedikt Herwerth ◽  
Germán Sierra ◽  
Hong-Hao Tu ◽  
J. Ignacio Cirac ◽  
Anne E. B. Nielsen
Keyword(s):  
Wave Function ◽  
Edge States ◽  
Laughlin Wave Function

STUDY ON THE MOST PROBABLE DISTRIBUTION FOR LAUGHLIN WAVE FUNCTIONS

1993 ◽  
Vol 07 (10) ◽  
pp. 679-687
Author(s):  
SHAOJIN QIN ◽  
ZHAOBIN SU ◽  
BINGSHEN WANG
Keyword(s):  
Wave Function ◽  
Triangular Lattice ◽  
Incompressible Liquid ◽  
Gaussian Approximation ◽  
Lattice Structure ◽  
Phase Fluctuation ◽  
Probable Distribution ◽  
Crystal Transition ◽  
Laughlin Wave Function ◽  
Most Probable Distribution

We show that, up to a global phase freedom, the most probable distribution of electrons given by the maxima of modulus square of Laughlin wave function (LWF), which is known to be a wave function for an incompressible liquid state of fractional Hall effect, has a triangular lattice structure. We introduce the Gaussian approximation for the modulus square of LWF. We find that the radial distribution function calculated from the Gaussian approximation has a form close to that of LWF at ν = 1, 1/3 and close to a crystal-like behavior when ν becomes smaller. We interprete the underlying physics to be that in the incompressible liquid regime, the "hidden" triangular lattice is smeared away by the quantum phase fluctuation, and as a precursor for liquid-crystal transition when the filling ν decreases towards the crystallization regime, it might manifest itself to be a sort of correlated short-range ordered density fluctuation.

LAUGHLIN'S WAVE FUNCTION AND ANGULAR MOMENTUM

2011 ◽  
Vol 25 (10) ◽  
pp. 1301-1357 ◽  
Author(s):  
KESHAV N. SHRIVASTAVA
Keyword(s):  
Wave Function ◽  
Angular Momentum ◽  
First Principles ◽  
Condensed Matter ◽  
Quantum Hall ◽  
Edge States ◽  
Coulomb Interactions ◽  
Bohm Effect ◽  
A Charge ◽  
Aharonov Bohm

In 1983, Laughlin reported a wave function which while using the first-principles kinetic energy and Coulomb interactions fractionalizes the charge of the electron so that a charge such as 1/3 occurs. Since then this wave function has been applied to many problems in condensed matter physics. An effort is made to review the literature dealing with Aharonov–Bohm effect, ground state, confinement, phase transitions, Wigner and Luttinger solids, edge states, Anderson's theory, statistics and anyons, etc. The importance of the angular momentum is pointed out and it is shown that Landau levels play an important role in understanding the fractions at which the plateaus occur in the quantum Hall effect.

scholarly journals Laughlin wave function and one-dimensional free fermions

1995 ◽  
Vol 52 (19) ◽  
pp. 13742-13744 ◽  
Author(s):  
Prasanta K. Panigrahi ◽  
M. Sivakumar
Keyword(s):  
Wave Function ◽  
Free Fermions ◽  
One Dimensional ◽  
Laughlin Wave Function

scholarly journals Geometric entanglement in the Laughlin wave function

2017 ◽  
Vol 19 (8) ◽  
pp. 083019
Author(s):  
Jiang-Min Zhang ◽  
Yu Liu
Keyword(s):  
Wave Function ◽  
Laughlin Wave Function

ENTANGLED STATE REPRESENTATIONS FOR DESCRIBING 2-DIMENSIONAL ELECTRON SYSTEM IN UNIFORM MAGNETIC FIELD

2004 ◽  
Vol 18 (20n21) ◽  
pp. 2771-2817 ◽  
Author(s):  
HONG-YI FAN
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Angular Momentum ◽  
Uniform Magnetic Field ◽  
Electron System ◽  
Entangled State ◽  
Dimensional Electron System ◽  
Einstein Podolsky Rosen ◽  
Set Up ◽  
Laughlin Wave Function

We review how to rely on the quantum entanglement idea of Einstein–Podolsky–Rosen and the developed Dirac's symbolic method to set up two kinds of entangled state representations for describing the motion and states of an electron in uniform magnetic field. The entangled states can be employed for conveniently expressing Landau wave function and Laughlin wave function with a fresh look. We analyze the entanglement involved in electron's coordinates (or momenta) eigenstates, and in the angular momentum-orbit radius entangled state. Various applications of these two representations, such as in developing angular momentum theory, squeezing mechanism, Wigner function and tomography theory for this system are presented. Thus the present review systematically summarizes a distinct approach for tackling this physical system.

QUASI-PROBABILITY DISTRIBUTION FOR LAUGHLIN STATE VECTORS

2001 ◽  
Vol 15 (14) ◽  
pp. 463-472 ◽  
Author(s):  
HONGYI FAN ◽  
JINGXIAN LIN
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Angular Momentum ◽  
Probability Distribution ◽  
Wigner Function ◽  
State Vector ◽  
Uniform Magnetic Field ◽  
Gauge Invariant ◽  
Wigner Operator ◽  
Laughlin Wave Function

Based on the gauge-invariant Wigner operator in <λ| representation (see Ref. 10), where the state |λ> can conveniently describe the motion of an electron in a uniform magnetic field, we provide an approach for identifying the corresponding state vector for Laughlin wave function and deriving the Wigner function (quasi-probability distribution) for the Laughlin state vector. The angular momentum-excited Laughlin state vectors are also obtained via <λ| representation.

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