2019/06/27 by Nicolas Rougerie, Rougerie, Nicolas · 1 citation
Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Magnetic properties of thin films #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Probability (math.PR) #Quantum and electron transport phenomena #Strongly Correlated Electrons (cond-mat.str-el) #Surface and Thin Film Phenomena #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.1906.11656
openalex publication_date 2019/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.