D-brane Dynamics and the Quantum Hall Effect

TL;DR

This paper analyzes a D-brane configuration modeling the quantum Hall effect, revealing interaction characteristics and ground state predictions, including Wigner crystal formation at low filling fractions and potential fractional quantum Hall states at higher fractions.

Contribution

It provides a detailed analysis of D-brane interactions in the quantum Hall model, highlighting the nature of the ground states based on filling fractions.

Findings

Interactions are repulsive, supporting quantum Hall liquid behavior.

Wigner crystal is favored at small filling fractions.

Potential for fractional quantum Hall states at larger rational filling fractions.

Abstract

We study the recently proposed D-brane configuration [hep-th/0010105] modeling the quantum Hall effect, focusing on the nature of the interactions between the charged particles. Our analysis indicates that the interaction is repulsive, which it should be for the ground state of the system to behave as a quantum Hall liquid. The strength of interactions varies inversely with the filling fraction, leading us to conclude that a Wigner crystal is the ground state at small nu. For larger rational nu (still less than unity), it is reasonable to expect a fractional quantum Hall ground state.