Laughlin's function on a cylinder: plasma analogy and representation as a quantum polymer

TL;DR

This paper analyzes Laughlin's fractional quantum Hall wave function on a cylinder, revealing a plasma analogy that results in a periodic density and a novel quantum polymer representation for calculating key properties.

Contribution

It introduces a quantum polymer representation of Laughlin's wave function on a cylinder, enabling new computational approaches for normalization and density in many-particle limits.

Findings

Plasma analogy leads to periodic density on a cylinder.

Wave function can be represented as a quantum polymer.

Method allows computation of normalization and density for large systems.

Abstract

We investigate Laughlin's fractional quantum Hall effect wave function in the cylinder geometry of Laughlin's integer quantum Hall effect argument, at filling factor 1/3. We show that the plasma analogy leads to a periodic density, and that the wave function admits a representation as a ``quantum polymer'', reminiscent of the quantum dimer model by Rokhsar and Kivelson. We explain how the representation can be exploited to compute the normalization and one-particle density in the limit of infinitely many particles.