Chern-Simons matrix model: coherent states and relation to Laughlin wavefunctions

TL;DR

This paper explores the Chern-Simons matrix model using coherent states, deriving many-body wavefunctions, and compares them to Laughlin wavefunctions, highlighting similarities at long distances but differences at short distances.

Contribution

It introduces a coherent state approach to analyze the Chern-Simons matrix model and compares resulting wavefunctions to Laughlin states, revealing partial agreement.

Findings

Agreement in long-distance behavior of wavefunctions

Differences in short-distance behavior

Coherent state representations yield distinct probability distributions

Abstract

Using a coherent state representation we derive many-body probability distributions and wavefunctions for the Chern-Simons matrix model proposed by Polychronakos and compare them to the Laughlin ones. We analyze two different coherent state representations, corresponding to different choices for electron coordinate bases. In both cases we find that the resulting probability distributions do not quite agree with the Laughlin ones. There is agreement on the long distance behavior, but the short distance behavior is different.