Incompressibility Estimates for the Laughlin Phase

Nicolas Rougerie (1) , Jakob Yngvason (2)

1 LPM2C - Laboratoire de physique et modélisation des milieux condensés
2 Erwin Schrödinger Institute for Mathematical Physics

This paper has its motivation in the study of the Fractional Quantum Hall Effect. We consider 2D quantum particles submitted to a strong perpendicular magnetic field, reducing admissible wave functions to those of the Lowest Landau Level. When repulsive interactions are strong enough in this model, highly correlated states emerge, built on Laughlin's famous wave function. We investigate a model for the response of such strongly correlated ground states to variations of an external potential. This leads to a family of variational problems of a new type. Our main results are rigorous energy estimates demonstrating a strong rigidity of the response of strongly correlated states to the external potential. In particular we obtain estimates indicating that there is a universal bound on the maximum local density of these states in the limit of large particle number. We refer to these as incompressibility estimates.

Domaines: Physique mathématique [math-ph]; Gaz Quantiques [cond-mat.quant-gas]; Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]; Electrons fortement corrélés [cond-mat.str-el]

Nicolas Rougerie, Jakob Yngvason. Incompressibility Estimates for the Laughlin Phase. 2014. ⟨hal-00950995v5⟩