Fractional quantization of Hall conductance

Tao, Ruibao; Thouless, D. J.

doi:10.1103/physrevb.28.1142

Cited by 175 publications

(149 citation statements)

References 9 publications

Supporting

Mentioning

145

Contrasting

Unclassified

Order By: Relevance

“…We find strong evidence that the (330) : 1/3 and (112) : 1/3 transitions are first order. The (330) : (112) transition appears to be very weakly first order, though we cannot definitely rule out a continuous transition. To determine the order of the transition we check for discontinuities in ∂ g E, where g = ∆ SAS , d tunes across the transition, as well as for divergences in the correlation length and discontinuities in local observables.…”

Section: B Order Of the Transitionsmentioning

confidence: 99%

“…In the "thin-torus" limit [112][113][114] the cylinder is effectively a one-dimensional spin-full fermion chain, the ground states reduce to the "root configurations".…”

Section: A the Interlayer-pfaffian Statementioning

confidence: 99%

“…We determine the phase diagram using the topological characterization explained in Sec. III C, and find three different Abelian phases [41]: decoupled ν = 1/3 bilayers (330) or the bilayer Laughlin phase, a bilayer-SU(2) symmetric spin-singlet hierarchy state (112), and a transversely polarized particle-hole conjugate of the Laughlin state 1/3. Fig.…”

Section: Abelian Phase Diagrammentioning

confidence: 99%

“…III C. First, we measure the momentum polarization M a in order to compute the shift S, which should take the values 3, 1 and 0 in the (330), (112) and 1/3 state, respectively. Fig.…”

Section: A Determination Of the Phasesmentioning

confidence: 99%

“…For small d/ℓ B and small ∆ SAS / e 2 ǫℓB , the system maintains SU(2) symmetry and resembles the usual ν = 2/3 state with spin. It has been known that the ground state in this case is a spin-singlet (112) state [25,[42][43][44] (for an explicit wavefunction see Refs. 41 and 45).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

et al. 2015

View full text Add to dashboard Cite

Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two sub-bands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling ν = 1/3 + 1/3. We first consider the Coulomb interaction at bilayer separation d, bilayer tunneling energy ∆SAS, and individual layer width w, where we find a phase diagram which includes three competing Abelian phases: a bilayer-Laughlin phase (two nearly decoupled ν = 1/3 layers); a bilayer-spin singlet phase; and a bilayer-symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases have also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the "interlayer-Pfaffian" phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that ν = 1/3 + 1/3 systems merit further experimental study. CONTENTS

show abstract

Section: B Order Of the Transitionsmentioning

confidence: 99%

“…In the "thin-torus" limit [112][113][114] the cylinder is effectively a one-dimensional spin-full fermion chain, the ground states reduce to the "root configurations".…”

Section: A the Interlayer-pfaffian Statementioning

confidence: 99%

Section: Abelian Phase Diagrammentioning

confidence: 99%

“…III C. First, we measure the momentum polarization M a in order to compute the shift S, which should take the values 3, 1 and 0 in the (330), (112) and 1/3 state, respectively. Fig.…”

Section: A Determination Of the Phasesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

et al. 2015

View full text Add to dashboard Cite

show abstract

Laughlin's function on a cylinder: plasma analogy and representation as a quantum polymer

Jansen¹,

Lieb

Seiler

2008

Physica Status Solidi (b)

View full text Add to dashboard Cite

PACS 73.43.Cd, 05.30.Fk We investigate Laughlin's fractional quantum Hall effect wave function in the cylinder geometry of Laughlin's integer quantum Hall effect argument, at filling factor 1/3. We show that the plasma analogy leads to a periodic density, and that the wave function admits a representation as a "quantum polymer", reminiscent of the quantum dimer model by Rokhsar and Kivelson. We explain how the representation can be exploited to compute the normalization and one-particle density in the limit of infinitely many particles.

show abstract

Liquid Site Model and Self‐Consistent Potentials in the Theory of Quantum Hall Effect

Ziep

Keiper

1987

Physica Status Solidi (b)

View full text Add to dashboard Cite

By %IKP and 1t. KEIPNRTo explain the quantum Hall effect (QHE) as a macroscopic quantum phenomenon with interference character the liquid site model is discussed in more detail. The calculated thermodynamic potential containing the magnetic field energy shows minima near the filling factors v = p / ( 2 n + 1) ( p = 1,2, ...; n = 0, 1,2, ...). Electron correlation in strong magnetic fields leads t o a local Hall potential satisfying the two-dimensional Laplace equation. The liquid site model permits t o discuss the necessity for a n optimum degree of disorder as well as the high precision attainable in &HE measurements.Um den Quantenhalleffekt (QHE) als makroskopisches Quantenphiinomen mit Interferenzcharakter zu erklaren, wird das "liquid site"-Model1 ausfiihrlicher diskutiert. Das berechnete thermodynamische Potential, das die magnetische Feldenergie enthalt, zeigt Minima in der Niihe des Fullfaktors v = p/(2n + 1) ( p = 1,2, ... ; n = 0, 1, 2, ...). Elektronenkorrelation in starken Magnetfeldern fiihrt zu einem lokalen Hallpotential, das der zweidimensionalen Laplacegleichung genugt. Das "liquid site"-Modell erlaubt, sowohl die Notwendigkeit fur einen optimalen Grad der Fehlordnung als auch die hohe Priizision, die in QHE-Messungen erreichbar ist, zu diskutieren.

show abstract

Fractional quantization of Hall conductance

Cited by 175 publications

References 9 publications

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

Laughlin's function on a cylinder: plasma analogy and representation as a quantum polymer

Liquid Site Model and Self‐Consistent Potentials in the Theory of Quantum Hall Effect

Contact Info

Product

Resources

About