Entanglement entropy of fractional quantum Hall systems with short range disorder

2015 ◽  
Vol 29 (12) ◽  
pp. 1550065 ◽  
Author(s):  
B. A. Friedman ◽  
G. C. Levine
Keyword(s):  
Short Range ◽  
Entanglement Entropy ◽  
Quantum Hall ◽  
Finite Size ◽  
Disorder Strength ◽  
Fractional Quantum ◽  
Finite Size Effects ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Liquid Transition

The critical value of the mobility for which the ν = 5/2 quantum Hall effect is destroyed by short range disorder is determined from an earlier calculation of the entanglement entropy. The value μ = 2.0 ×106 cm 2/ Vs agrees well with experiment. This agreement is particularly significant in that there are no adjustable parameters. Entanglement entropy versus disorder strength for ν = 1/2, ν = 9/2 and ν = 7/3 is calculated. For ν = 1/2 there is no evidence for a transition for the disorder strengths considered; for ν = 9/2 there appears to be a stripe-liquid transition. For ν = 7/3 there again appears to be a transition at similar value of the disorder strength as the ν = 5/2 transition but there are stronger finite size effects.

scholarly journals Short and long ranged impurities in fractional quantum Hall systems

2018 ◽  
Vol 32 (30) ◽  
pp. 1850338 ◽  
Author(s):  
B. A. Friedman
Keyword(s):  
Long Range ◽  
Short Range ◽  
Physical Mechanism ◽  
Quantum Hall ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Quantitative Understanding

Short- and long-range impurities have been examined for fractional quantum Hall systems. There appears to be a consistent computational picture for short-range impurities. In the case of long-range impurities, calculations agree qualitatively with experiment, in that the critical mobility is very sensitive to long-range impurities and the critical mobility for long range impurities is larger than the critical mobility for short-range impurities. The physical mechanism of this sensitivity and a quantitative understanding remain a challenging computational issue.

SPIN STRUCTURES IN INHOMOGENEOUS FRACTIONAL QUANTUM HALL SYSTEMS

2004 ◽  
Vol 18 (27n29) ◽  
pp. 3871-3874 ◽  
Author(s):  
KAREL VÝBORNÝ ◽  
DANIELA PFANNKUCHE
Keyword(s):  
Ground State ◽  
Quantum Hall ◽  
Exact Diagonalization ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Spin Structures ◽  
Quantum Hall Systems ◽  
Magnetic Inhomogeneities ◽  
Spin Singlet ◽  
Spin Polarized

Transitions between spin polarized and spin singlet incompressible ground state of quantum Hall systems at filling factor 2/3 are studied by means of exact diagonalization with eight electrons. We observe a stable exactly half–polarized state becoming the absolute ground state around the transition point. This might be a candidate for the anomaly observed during the transition in optical experiments. The state reacts strongly to magnetic inhomogeneities but it prefers stripe–like spin structures to formation of domains.

scholarly journals The Fermion–Boson transformation in fractional quantum Hall systems

2001 ◽  
Vol 9 (4) ◽  
pp. 701-708 ◽  
Author(s):  
John J. Quinn ◽  
Arkadiusz Wójs ◽  
Jennifer J. Quinn ◽  
Arthur T. Benjamin
Keyword(s):  
Quantum Hall ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems

scholarly journals COLLECTIVE COORDINATE ACTION FOR CHARGED SIGMA-MODEL VORTICES IN FINITE GEOMETRIES

1993 ◽  
Vol 08 (19) ◽  
pp. 1815-1820 ◽  
Author(s):  
THEODORE J. ALLEN
Keyword(s):  
Sigma Model ◽  
Quantum Hall ◽  
Finite Size ◽  
Effective Field ◽  
Finite Geometries ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Collective Coordinate ◽  
The Green Function ◽  
Laughlin Wave Function

We apply the method of Lund to formulate a variational principle for the motion of charged vortices in an effective nonlinear Schrödinger field theory describing finite size two-dimensional quantum Hall samples under the influence of an arbitrary perpendicular magnetic field. Freezing out variations in the modulus of the effective field yields a U(1) sigma-model. A duality transformation on the sigma-model reduces the problem to finding the Green function for a related electrostatics problem. This duality connects the plasma analogy to the Laughlin wave function directly to a vortex gas description of the fractional quantum Hall effect.

Topological Aspects of Quantum Hall Fluid and Berry Phase

1998 ◽  
Vol 12 (26) ◽  
pp. 2649-2707 ◽  
Author(s):  
Banasri Basu ◽  
P. Bandyopadhyay
Keyword(s):  
Quantum Hall Effect ◽  
Berry Phase ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Chiral Anomaly ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Characteristic Features

We have analyzed here the recent development towards our understanding of the Integral and Fractional Quantum Hall effect. It has been pointed out that the chiral anomaly and Berry phase approach embraces in a unified way the whole spectrum of quantum Hall systems with their various characteristic features. This formalism also helps us to understand the edge states observed in Hall fluids. It is argued that Hall fluids with even denominator filling factor leads to the non-Abelian Berry phase.

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