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The fractional quantum Hall effect and the spherical shell model

Joseph N. Ginocchio

Published Jan 1, 1993• 1 citation
OpenAlex

Abstract

We review the fractional quantum Hall effect in a spherical geometry and propose an ansatz for the many electron wavefunction which may explain the fractional quantum Hall effect.

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On the ground state of fractional quantum Hall effect

Ahmed Jellal

The paper has bene withdrawn by the author.

arXiv:cond-mat/9810086•Oct 8, 1998•0 citations
With the use of Haldane's spherical model, the fractional quantum Hall effect is studied by means of large-scale configuration-interaction calculations. The exact wave function and the ground-state energy are computed numerically up to ten electrons for filling \ensuremath{\nu}=(1/3), and up to seven electrons for filling \ensuremath{\nu}=(1/5). Quasiparticle, quasihole, and exciton energies are computed. The mutual relation between wave functions on the sphere and wave functions on the disk is fully analyzed. A wave function originally proposed by Halperin for the disk geometry is tested on the sphere; the numerical results up to six electrons for \ensuremath{\nu}=(2/5) and \ensuremath{\nu}=(2/9) are favorable.
In this letter, we discuss the recently proposed fractional quantum Hall effect in the absence of Landau levels. It is shown that the parton construction can explain all properties of 1/3 state, including the effective charge of quasi-particles, their statistics and the many-body ground-state degeneracy. The low energy description of these states has been discussed. We also generalize our model to construct the hierarchical quantum Hall states at filling fractions other than 1/m1/m1/m.
Neural network fractional quantum Hall (FQH) states offer a promising alternative for capturing Landau level (LL) mixing and for understanding FQH physics, yet the incorporation of physical priors has so far been limited to the minimal exact constraints built into the ansatz. Working in spherical geometry, we show that the network's flexibility suffers both when only minimal additional physical priors are supplied and when priors such as flux attachment are imposed rigidly. In the former case, the monopole harmonic product orbital (MHPO) ansatz is difficult to optimize, whereas in the latter, the expressivity of the neural network is restricted. We therefore propose the orbital pair matrix factor MHPO (MHPO-M) ansatz, which balances physical priors against flexibility by not only replacing the fixed Laughlin structure with learnable pair factors but also making them dependent on both the electron configurations and the orbitals. Across ν=1/5ν=1/5ν=1/5, 1/31/31/3, and 2/52/52/5, MHPO-M achieves the lowest variational energy among the tested variants, and a factorized orbital readout based on it enables scaling to 35 electrons, with energies competitive with trends inferred from three-LL exact-diagonalization results. These results demonstrate that physical priors can be appropriately incorporated without sacrificing the flexibility of neural network wavefunctions, opening a promising path toward accurate, scalable modeling of FQH systems with LL mixing.