Hamiltonian Theory of Anisotropic Fractional Quantum Hall States

TL;DR

This paper extends the Hamiltonian theory of fractional quantum Hall states to include anisotropic cases, providing quantitative analysis and agreement with experimental and previous theoretical results.

Contribution

It generalizes the operator-based Hamiltonian theory to anisotropic FQH states, enabling computation of effective anisotropies and comparison with experiments.

Findings

Good agreement with previous theoretical results on anisotropy.

Effective anisotropies match experimental observations.

The theory applies to both lowest and first Landau levels.

Abstract

Rotationally invariant fractional quantum Hall (FQH) states have long been understood in terms of composite bosons or composite fermions. Recent investigations of both incompressible and compressible states in highly tilted fields, which renders them anisotropic, have revealed puzzling features which have so far defied quantitative explanation. The author's work with R. Shankar in constructing and analyzing an operator-based theory in the rotationally invariant FQHE is generalized here to the anisotropic case. We compute the effective anisotropies of many principal fraction states in the lowest and the first Landau levels and find good agreement with previous theoretical results. We compare the effective anisotropy in a model potential with finite sample thickness and find good agreement with experimental results.