# Stability of the Laughlin phase against long-range interactions

## TL;DR

This paper proves that for small pair interactions and large particle numbers, the Laughlin phase remains stable, with minimizers characterized by uncorrelated quasi-holes superimposed on Laughlin's wave-function.

## Contribution

It demonstrates the stability of the Laughlin phase against long-range interactions and characterizes the form of minimizers in this regime.

## Key findings

- Minimizers can be approximated by uncorrelated quasi-holes for small interactions.
- Stability of the Laughlin phase is maintained asymptotically for large particle numbers.
- The analysis applies to a class of classical energy functionals in quantum Hall models.

## Abstract

A natural, "perturbative", problem in the modelization of the fractional quantum Hall effect is to minimize a classical energy functional within a variational set based on Laughlin's wave-function. We prove that, for small enough pair interactions, and asymptotically for large particle numbers, a minimizer can always be looked for in the particular form of uncorrelated quasi-holes superimposed to Laughlin's wave-function.