Exact results for the fractional quantum Hall effect with general interactions

Trugman, S. A.; Kivelson, Steven

doi:10.1103/physrevb.31.5280

Cited by 292 publications

(318 citation statements)

References 9 publications

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“…In order to control J in the infinite plane with an external parameter, we introduce a central harmonic potential which confines the particles 9) where G is the Gibbs free energy. Indeed, this modification is physical since it corresponds precisely to the effect of the neutralizing positive charged background [22]. The harmonic potential can be written in terms of a and b's and therefore of J and H 10) where λ = α(α + 2).…”

Section: Landau Levelsmentioning

confidence: 99%

“…* Note that the condition of magnetic translation invariance, L −1,0 Ψ = 0, has been previously recognized as a necessary condition for incompressibility of the ground state [22][20].…”

Section: Eqs (37) Precisely State the Incompressibility Conditions mentioning

confidence: 99%

“…It describes electrons constrained to the lowest Landau level and interacting via the two-body repulsive potential 22) where V k is the short-range potential defined previously. A more explicit form of its action on the holomorphic wave function is given by…”

Section: Exactness and Infinite Symmetry Of Laughlin's Wave Functionmentioning

confidence: 99%

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Infinite symmetry in the quantum Hall effect

1993

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Free planar electrons in a uniform magnetic field are shown to possess the symmetry of area-preserving diffeomorphisms (W -infinity algebra). Intuitively, this is a consequence of gauge invariance, which forces dynamics to depend only on the flux. The infinity of generators of this symmetry act within each Landau level, which is infinite-dimensional in the thermodynamical limit. The incompressible ground states corresponding to completely filled Landau levels (integer quantum Hall effect) are shown to be infinitely symmetric, since they are annihilated by an infinite subset of generators. This geometrical characterization of incompressibility also holds for fractional fillings of the lowest level (simplest fractional Hall effect) in the presence of Haldane's effective two-body interactions. Although these modify the symmetry algebra, the corresponding incompressible ground states proposed by Laughlin are again symmetric with respect to the modified infinite algebra.

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Section: Landau Levelsmentioning

confidence: 99%

“…* Note that the condition of magnetic translation invariance, L −1,0 Ψ = 0, has been previously recognized as a necessary condition for incompressibility of the ground state [22][20].…”

Section: Eqs (37) Precisely State the Incompressibility Conditions mentioning

confidence: 99%

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Infinite symmetry in the quantum Hall effect

1993

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“…[6] [7] In order to compare the α = 0 with the α = 0 states we performed Monte Carlo simulations of the equivalent classical plasmas with 200 particles in the disk geometry, and compared the energies of candidate ground states. (We believe that improvement of the wavefunction by, for example, quantum Monte Carlo techniques [8] will not affect energy differences very much.)…”

mentioning

confidence: 99%

Broken rotation symmetry in the fractional quantum Hall system

Musaelian

Joynt

1996

J. Phys.: Condens. Matter

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We demonstrate that the two-dimensonal electron system in a strong perpendicular magnetic field has stable states which break rotational but not translational symmetry. The Laughlin fluid becomes unstable to these states in quantum wells whose thickness exceeds a critical value which depends on the electron density. The order parameter at 1/3 reduced density resembles that of a nematic liquid crystal, in that a residual two-fold rotation axis is present in the low symmetry phase. At filling factors 1/5 and 1/7, there are states with four-and six-fold axes, as well. We discuss the experimental detection of these phases.

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“…Hamiltonians with ultra-short interactions [9] for which Laughlin wave-functions are exact ground state wave-functions have been known for years. We have also been able to construct gauge models [10] for which the Laughlin wave-functions are exact ground states.…”

mentioning

confidence: 99%

Exactly solvable models in arbitrary dimensions

Ghosh

Rao

1998

Physics Letters A

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We construct a new class of quasi-exactly solvable many-body Hamiltonians in arbitrary dimensions, whose ground states can have any correlations we choose. Some of the known correlations in one dimension and some recent novel correlations in two and higher dimensions are reproduced as special cases. As specific interesting examples, we also write down some new models in two and higher dimensions with novel correlations.

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Exact results for the fractional quantum Hall effect with general interactions

Cited by 292 publications

References 9 publications

Infinite symmetry in the quantum Hall effect

Infinite symmetry in the quantum Hall effect

Broken rotation symmetry in the fractional quantum Hall system

Exactly solvable models in arbitrary dimensions

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