Geodesic
On the Laughlin function and its perturbations
Rougerie, Nicolas1
1Université Grenoble Alpes & CNRS LPMMC (UMR 5493) B.P. 166 F-38042 Grenoble France
Séminaire Laurent Schwartz — EDP et applications (2018-2019), Talk no. 2, 17 p.

See the original proceeding notice from the Numdam source

The Laughlin state is an ansatz for the ground state of a system of 2D quantum particles submitted to a strong magnetic field and strong interactions. The two effects conspire to generate strong and very specific correlations between the particles.

I present a mathematical approach to the rigidity these correlations display in their response to perturbations. This is an important ingredient in the theory of the fractional quantum Hall effect. The main message is that potentials generated by impurities and residual interactions can be taken into account by generating uncorrelated quasi-holes on top of Laughlin’s wave-function.

An appendix contains a conjecture (not due to me) that should be regarded as a major open mathematical problem of the field, relating to the spectral gap of a certain zero-range interaction.

Expository text based on joint works with Elliott H. Lieb, Alessandro Olgiati, Sylvia Serfaty and Jakob Yngvason.

Published online:
DOI: 10.5802/slsedp.131

Rougerie, Nicolas  1

1 Université Grenoble Alpes & CNRS LPMMC (UMR 5493) B.P. 166 F-38042 Grenoble France 
Rougerie, Nicolas. On the Laughlin function and its perturbations. Séminaire Laurent Schwartz — EDP et applications (2018-2019), Talk no. 2, 17 p.. doi: 10.5802/slsedp.131
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