The Laughlin liquid in an external potential

TL;DR

This paper investigates how the Laughlin state, a key quantum Hall wave function, responds to external trapping and disorder, providing precise energy bounds and modifications involving quasi-holes.

Contribution

It derives an exact large N energy bound for perturbed Laughlin states under external potentials, matching previous lower bounds and introducing quasi-hole modifications.

Findings

Established a sharp upper bound for the ground state energy in external potentials.

Demonstrated that the bound can be achieved by adding quasi-holes to the Laughlin state.

Confirmed the bound's independence from the shape of the confining potential.

Abstract

We study natural perturbations of the Laughlin state arising from the effects of trapping and disorder. These are N-particle wave functions that have the form of a product of Laughlin states and analytic functions of the N variables. We derive an upper bound to the ground state energy in a confining external potential, matching exactly a recently derived lower bound in the large N limit. Irrespective of the shape of the confining potential, this sharp upper bound can be achieved through a modification of the Laughlin function by suitably arranged quasi-holes.