Wave functions for arbitrarily Polarized Quantum Hall States

TL;DR

This paper derives wave functions for quantum Hall states with arbitrary polarization using a doublet model, confirming known wave functions and quantization of Hall conductivity, and explaining non-analyticity and quantum fluctuations.

Contribution

It introduces a doublet model to describe arbitrarily polarized quantum Hall states, recovering known wave functions and analyzing their properties.

Findings

Wave functions for arbitrarily polarized states derived

Hall conductivity quantized at specific filling fractions

Quantum fluctuations restore the Kohn mode

Abstract

We determine the wave functions for arbitrarily polarized quantum Hall states by employing the doublet model which has been proposed recently to describe arbitrarily polarized quantum Hall states. Our findings recover the well known fully polarized Laughlin wave functions and unpolarized Halperin wave function for the filling fraction $\nu =2/5$. We have also confirmed by an explicit One-loop computation that the Hall conductivity does indeed get quantized at those filling fractions that follow from the model. Finally, we have given a physical picture for the non-analytic nature of the wave functions, and shown that quantum fluctuations restore the Kohn mode.