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Pré-Publication, Document De Travail Année : 2016

Rigidity of the Laughlin liquid

Résumé

We consider general N-particle wave functions that have the form of a product of the Laughlin state with filling factor $1/\ell$ and an analytic function of the N variables. This is the most general form of a wave function that can arise through a perturbation of the Laughlin state by external potentials or impurities, while staying in the lowest Landau level and maintaining the strong correlations of the original state. We show that the perturbation can only shift or lower the 1-particle density but nowhere increase it above a maximum value. Regardless of the analytic prefactor, the density satisfies the same bound as the Laughlin function itself, i.e. $(\pi \ell) ^{-1}$ in the limit of large particle number. Consequences of this incompressibility bound for the response of the Laughlin state to external fields are discussed. Our theorems apply equally to bosonic and fermionic states.
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Dates et versions

hal-01364206 , version 1 (12-09-2016)
hal-01364206 , version 2 (21-09-2016)
hal-01364206 , version 3 (29-11-2016)
hal-01364206 , version 4 (08-02-2017)
hal-01364206 , version 5 (31-05-2018)

Identifiants

Citer

Elliott H. Lieb, Nicolas Rougerie, Jakob Yngvason. Rigidity of the Laughlin liquid. 2016. ⟨hal-01364206v2⟩
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