Explicit Relation of Quantum Hall Effect and Calogero-Sutherland Model

TL;DR

This paper establishes an explicit connection between the quantum Hall effect's Laughlin state and the Calogero-Sutherland model by expressing wave functions in a one-dimensional framework, revealing new insights into their relationship.

Contribution

It introduces a novel 1D representation of Laughlin states, linking them directly to Calogero-Sutherland models across various geometries.

Findings

Laughlin state expressed as a deformation of Calogero-Sutherland ground state

Different geometries correspond to different 1D $1/r^2$ interaction models

Provides a unified framework connecting quantum Hall states and 1D integrable models

Abstract

Explicit relation between Laughlin state of the quantum Hall effect and one-dimensional(1D) model with long-ranged interaction ($1/r^2$) is discussed. By rewriting lowest Landau level wave functions in terms of 1D representation, Laughlin state can be written as a deformation of the ground state of Calogero-Sutherland model. Corresponding to Laughlin state on different geometries, different types of 1D $1/r^2$ interaction models are derived.