Spectrum of the Hermitian Wilson-Dirac Operator for a Uniform Magnetic Field in Two Dimensions

Abstract

It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An explicit formula for the secular equations is given in term of a set of polynomials. The spectrum exhibits a fractal structure in the infinite volume limit. An exact result concerning the index theorem for the overlap Dirac operator is obtained.

8 pages, latex, 3 eps figures, minor corrections

References in corpus (3)

• Fermions on tori in uniform abelian fields
• More about the axial anomaly on the lattice
• A Numerical Study of Spectral Flows of Hermitian Wilson-Dirac Operator and the Index Theorem in Abelian Gauge Theories on Finite Lattices

Cited by in corpus (2)

• More about the axial anomaly on the lattice
• Wess-Zumino-Witten term on the lattice