Slater Decomposition of Laughlin States

TL;DR

This paper presents a method to decompose Laughlin states into Slater determinants using symmetric group characters, revealing symmetries and identifying dominant states in the large particle limit.

Contribution

It introduces a general formula for expansion coefficients of Laughlin states in the Slater basis, highlighting their symmetries and physical relevance.

Findings

Derived a formula for expansion coefficients using symmetric group characters.

Identified dominant Slater states with correct density and filling fraction in the large N limit.

Revealed symmetries in the coefficients of Laughlin wavefunctions.

Abstract

The second-quantized form of the Laughlin states for the fractional quantum Hall effect is discussed by decomposing the Laughlin wavefunctions into the $N$-particle Slater basis. A general formula is given for the expansion coefficients in terms of the characters of the symmetric group, and the expansion coefficients are shown to possess numerous interesting symmetries. For expectation values of the density operator it is possible to identify individual dominant Slater states of the correct uniform bulk density and filling fraction in the physically relevant $N\to\infty$ limit.