Edge Hamiltonian for Free Fermion Quantum Hall Models

TL;DR

This paper confirms that Kitaev's proposed edge Hamiltonian accurately models the edge modes of quantum Hall systems in free-fermion, translation-invariant settings, capturing the correct chirality of edge states.

Contribution

It demonstrates that Kitaev's microscopic edge Hamiltonian construction works for translation-invariant free-fermion models, accurately reproducing edge modes with proper chirality.

Findings

Edge Hamiltonian exhibits only edge modes

Edge modes have correct chirality

Construction valid for translation-invariant free-fermion systems

Abstract

We investigate a proposal of Kitaev for a microscopic construction of a Hamiltonian intended to describe the edge dynamics of a quantum Hall system. We show that the construction works in the setting of translation-invariant free-fermion Hamiltonians. In this case, the resulting edge Hamiltonian exhibits only edge modes, and these modes have the correct chirality.