Interaction and dynamical binding of spin waves or excitons in quantum Hall systems

TL;DR

This paper investigates the interactions between spin waves and excitons in quantum Hall systems, revealing that their effective interactions differ from simple models and lead to phenomena like dynamical binding and linear excitation spectra.

Contribution

It provides a detailed numerical analysis of the effective interactions between spin waves and excitons, highlighting their unique power-law behavior and implications for quantum Hall excitations.

Findings

Spin waves moving in the same direction attract and bind dynamically.

Interaction pseudopotentials follow power laws V(k) ~ k^alpha at small k.

High alpha value (~4) explains linear bands in spin excitation spectra.

Abstract

Interaction between spin waves (or excitons) moving in the lowest Landau level is studied using numerical diagonalization. Becuse of complicated statistics obeyed by these composite particles, their effective interaction is completely different from the dipole-dipole interaction predicted in the model of independent (bosonic) waves. In particular, spin waves moving in the same direction attract one another which leads to their dynamical binding. The interaction pseudopotentials V_[up,up](k) and V_[up,down](k) for two spin waves with equal wavevectors k and moving in the same or opposite directions have been calculated and shown to obey power laws V(k) ~ k^alpha at small k. A high value of alpha_[up,up]~4 explains the occurrence of linear bands in the spin excitation spectra of quantum Hall droplets.