Incompressibility estimates for the Laughlin phase, part II

TL;DR

This paper establishes a universal local density upper bound for a broad class of Laughlin-based fractional quantum Hall states, aiding understanding of their response to external potential variations.

Contribution

It extends previous results by providing a density bound applicable to a wider class of wave-functions without additional assumptions.

Findings

Proves a universal local density upper bound for Laughlin states.

The bound applies to a broad class of wave-functions with minimal assumptions.

Facilitates analysis of fractional quantum Hall phases under external perturbations.

Abstract

We consider fractional quantum Hall states built on Laughlin's original N-body wave-functions, i.e., they are of the form holomorphic times gaussian and vanish when two particles come close, with a given polynomial rate. Such states appear naturally when looking for the ground state of 2D particles in strong magnetic fields, interacting via repulsive forces and subject to an external potential due to trapping and/or disorder. We prove that all functions in this class satisfy a universal local density upper bound, in a suitable weak sense. Such bounds are useful to investigate the response of fractional quantum Hall phases to variations of the external potential. Contrary to our previous results for a restricted class of wave-functions, the bound we obtain here is not optimal, but it does not require any additional assumptions on the wave-function, besides analyticity and symmetry of the pre-factor modifying the Laughlin function.