A new approach to the ground state of quantum Hall systems. Basic principles

Mikhaǐlov, S. A.

doi:10.1016/s0921-4526(00)00769-9

Cited by 23 publications

(21 citation statements)

References 61 publications

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“…As in the half-filling case, both methods yield for filling 1 / 3 an energy correction about ten times larger than that for the WS state, 6 adding support to the conjecture that at all fillings the high electron overlap of the CDW enhances significantly the cohesive energy corrections. 7,9 This reopens the case for the CDW state as a serious candidate for precursor to the true ground state in a perturbative approach in the thermodynamic limit.…”

Section: Introductionmentioning

confidence: 83%

Analytic mean-field charge-density-wave solution atν=1∕3: Composite-fermion-like subbands and correlation effects

Cabo

Claro

2004

Phys. Rev. B

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An analytic solution of the Hartree-Fock problem for a 2DEG at filling 1 / 3 and half an electron per unit cell is presented. The Coulomb interaction dynamically breaks the first Landau level in three narrow subbands, one of which is fully occupied and the others empty, as in the composite fermion model. Strong correlations are expected owing to large charge density overlap between neighboring plaquettes. Numerical evaluations show an enhancement of the cohesive correlation energy, bringing the energy per particle to the proximity of that obtained in competing variational models. Correlations are long range, requiring over 98 particles in numerical computations to approach convergence.

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Section: Introductionmentioning

confidence: 83%

Analytic mean-field charge-density-wave solution atν=1∕3: Composite-fermion-like subbands and correlation effects

Cabo

Claro

2004

Phys. Rev. B

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“…(The calculations have been done correctly [7,18], of course, but without comments on the seemingly incorrect sign of the "angular momentum. ")…”

Section: Changes Of Signmentioning

confidence: 99%

Angular momentum in the fractional quantum Hall effect

Enk

2020

American Journal of Physics

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It is an underappreciated fact that the wave functions of electrons in the lowest Landau level describing the fractional quantum Hall effect have an azimuthal dependence ∝ exp(−imφ) with m ≥ 0, seemingly in contradiction with the classical electron having positive angular momentum. We show here that the gauge-independent meaning of that quantum number m is not angular momentum, but that it quantizes the distance of the center of the electron's orbit from the origin, and that the physical angular momentum of the electron is positive and independent of m in the lowest Landau levels. We note that textbooks and the original literature have managed to come up with wave functions that do have the seemingly correct azimuthal form ∝ exp(+imφ) but only on account of changing a sign on the way to that result.

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“…Since the drift equations are just first-order differential equations, they can be solved easily by any numerical method to arrive at their statinary points. In the above case, the stationary points can be gotten simply by setting the τ -derivatives to zero: which has been extensively discussed in the literature [4,23,24], notably by Yannouleas and…”

Section: Spontaneous Symmetry-breaking Wave Functionsmentioning

confidence: 99%

Solving fermion problems without solving the sign problem: Symmetry-breaking wave functions from similarity-transformed propagators for solving two-dimensional quantum dots

Chin

2020

Phys. Rev. E

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It is well known that the use of the primitive second-order propagator in Path Integral Monte Carlo calculations of many-fermion systems leads to the sign problem. In this work, we show that by using the similarity-transformed Fokker-Planck propagator, it is possible to solve for the ground state of a large quantum dot, with up to 100 polarized electrons, without solving the sign problem.These similarity-transformed propagators naturally produce rotational symmetry-breaking ground state wave functions previously used in the study of quantum dots and quantum Hall effects.However, instead of localizing the electrons at positions which minimize the potential energy, this derivation shows that they should be located at positions which maximize the bosonic ground state wave function. Further improvements in the energy can be obtained by using these as initial wave functions in a Ground State Path-Integral Monte Carlo calculation with second and fourth-order propagators.

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A new approach to the ground state of quantum Hall systems. Basic principles

Cited by 23 publications

References 61 publications

Analytic mean-field charge-density-wave solution atν=1∕3: Composite-fermion-like subbands and correlation effects

Analytic mean-field charge-density-wave solution atν=1∕3: Composite-fermion-like subbands and correlation effects

Angular momentum in the fractional quantum Hall effect

Solving fermion problems without solving the sign problem: Symmetry-breaking wave functions from similarity-transformed propagators for solving two-dimensional quantum dots

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