A Field Theory for the Read Operator

TL;DR

This paper develops a new quantum field theory for quantum Hall systems that simplifies previous models by not restricting to the lowest Landau level, and demonstrates that mean-field solutions correspond to Laughlin states.

Contribution

It introduces a simplified, exact formalism for quantum Hall systems using a modified bosonic field theory that captures Laughlin states as mean-field solutions.

Findings

Mean-field solutions correspond to Laughlin states

New formalism simplifies previous models

Exact dynamics of bosonic field operators derived

Abstract

We introduce a new field theory for studying quantum Hall systems. The quantum field is a modified version of the bosonic operator introduced by Read. In contrast to Read's original work we do {\em not} work in the lowest Landau level alone, and this leads to a much simpler formalism. We identify an appropriate canonical conjugate field, and write a Hamiltonian that governs the exact dynamics of our bosonic field operators. We describe a Lagrangian formalism, derive the equations of motion for the fields and present a family of mean-field solutions. Finally, we show that these mean field solutions are precisely the Laughlin states. We do not, in this work, address the treatment of fluctuations.