Laughlin's wave functions, Coulomb gases and expansions of the discriminant

TL;DR

This paper explores Laughlin's wave functions in the fractional quantum Hall effect, analyzing their normalization via plasma models, effects of quadrupolar fields, and methods for expanding and counting Slater determinant states.

Contribution

It introduces new methods for expanding Laughlin's wave functions and provides estimates for plasma free energy under quadrupolar perturbations.

Findings

Effect of quadrupolar field on plasma free energy

Sum rules for expansion coefficients of wave functions

Counting Slater states using integral polytope theory

Abstract

In the context of the fractional quantum Hall effect, we investigate Laughlin's celebrated ansatz for the groud state wave function at fractional filling of the lowest Landau level. Interpreting its normalization in terms of a one component plasma, we find the effect of an additional quadrupolar field on the free energy, and derive estimates for the thermodynamically equivalent spherical plasma. In a second part, we present various methods for expanding the wave function in terms of Slater determinants, and obtain sum rules for the coefficients. We also address the apparently simpler question of counting the number of such Slater states using the theory of integral polytopes.