The spectrum of the Hermitian Wilson-Dirac operator is investigated for an arbitrary uniform magnetic field in two dimensions. It can be described by a relativistic analogue of the Harper equation. The index of the overlap Dirac operator is obtained directly from the spectral asymmetry of the relativistic Harper system. It coincides with the topological charge if the field strength is equal to or less than $\pi /2.\mathrm{}$

• Received 14 June 2002

DOI:https://doi.org/10.1103/PhysRevD.67.025015