EXPLICIT SOLUTIONS OF THE BETHE-ANSATZ EQUATIONS FOR BLOCH ELECTRONS IN A MAGNETIC-FIELD

For Bloch electrons in a magnetic field, explicit solutions are obtained at the center of the spectrum for the Bethe ansatz equations of Wiegmann and Zabrodin. When the magnetic flux per plaquette is 1/Q with Q an odd integer, distribution of the roots of the Bethe ansatz equation is uniform except at two points on the unit circle in the complex plane. For the semiclassical limit Q --> infinity, the wave function is \psi(x)\2 = (2/sin pix), which is critical and unnormalizable. For the golden-mean flux, the distribution of roots has exact self-similarity and the distribution function is nowhere differentiable. The corresponding wave function also shows a clear self-similar structure.