Rigidity of the Laughlin liquid

Understand

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.
• Consequences of this bound for the response of the Laughlin state to external fields are discussed.