Edge Theories for Polarized Quantum Hall States

TL;DR

This paper develops effective low-energy theories for edge modes in polarized quantum Hall states, incorporating gauge symmetry and spin rotation invariance, and finds chiral edge spin waves with distinct properties from bulk modes.

Contribution

It introduces a new framework for describing edge excitations in polarized quantum Hall states based on bosonic mean field theories and symmetry considerations.

Findings

Edge spin waves are chiral in generic cases.

Spin stiffness at the edge differs from the bulk.

Results agree with Hartree-Fock for fully polarized ν=1 state.

Abstract

Starting from recently proposed bosonic mean field theories for fully and partially polarized quantum Hall states, we construct corresponding effective low energy theories for the edge modes. The requirements of gauge symmetry and invariance under global O(3) spin rotations, broken only by a Zeeman coupling, imply boundary conditions that allow for edge spin waves. In the generic case, these modes are chiral, and the spin stiffness differs from that in the bulk. For the case of a fully polarized $\nu=1$ state, our results agree with previous Hartree-Fock calculations.