On the Laughlin function and its perturbations

TL;DR

This paper presents a mathematical analysis of the robustness of Laughlin's wave-function in the fractional quantum Hall effect, showing how perturbations like impurities can be modeled with uncorrelated quasi-holes.

Contribution

It introduces a mathematical approach to understanding the rigidity of correlations in the Laughlin state under perturbations, advancing the theoretical framework of the fractional quantum Hall effect.

Findings

Potentials from impurities can be modeled by uncorrelated quasi-holes.

The correlations in the Laughlin state exhibit rigidity against perturbations.

An open conjecture relates to the spectral gap of a zero-range interaction.

Abstract

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.