Rigidity of the Laughlin liquid

TL;DR

This paper proves that perturbations of the Laughlin state cannot increase the local particle density beyond a certain maximum, highlighting the rigidity of the Laughlin liquid under external influences.

Contribution

It establishes a fundamental density bound for wave functions perturbing the Laughlin state, extending understanding of its stability and response to external potentials.

Findings

Perturbations cannot increase local density above a maximum.

External potentials can only shift or lower the density.

The Laughlin state exhibits rigidity against external perturbations.

Abstract

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.