Communications in Mathematical Physics

, Volume 336, Issue 3, pp 1109–1140 | Cite as

Incompressibility Estimates for the Laughlin Phase



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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Université Grenoble 1 and CNRS, LPMMC, UMR 5493GrenobleFrance
  2. 2.Fakultät für PhysikUniversität WienViennaAustria
  3. 3.Erwin Schrödinger Institute for Mathematical PhysicsViennaAustria

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