Letters in Mathematical Physics

, Volume 108, Issue 4, pp 1007–1029 | Cite as

The Laughlin liquid in an external potential

  • Nicolas Rougerie
  • Jakob Yngvason


We study natural perturbations of the Laughlin state arising from the effects of trapping and disorder. These are N-particle wave functions that have the form of a product of Laughlin states and analytic functions of the N variables. We derive an upper bound to the ground state energy in a confining external potential, matching exactly a recently derived lower bound in the large N limit. Irrespective of the shape of the confining potential, this sharp upper bound can be achieved through a modification of the Laughlin function by suitably arranged quasi-holes.


Fractional quantum hall effect Laughlin states Quasi-holes 

Mathematics Subject Classification




We thank Elliott H. Lieb for helpful remarks. N. Rougerie received financial support from the French ANR Project ANR-13-JS01-0005-01.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Université Grenoble Alpes and CNRSLPMMC (UMR 5493)GrenobleFrance
  2. 2.Faculty of PhysicsUniversity of ViennaViennaAustria

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