Fermions in an anisotropic random magnetic field

Abstract

We study the localization of fermions in an anisotropic random magnetic field in two dimensions. It is assumed that the randomness in a particular direction is stronger than those in the other directions. We consider a network model of zero field contours, where there are two types of randomness - the random tunneling matrix element at the saddle points and unidirectional random variation of the number of fermionic states following zero field contours. After averaging over the random complex tunneling amplitude, the problem is mapped to an SU(2N) random exchange quantum spin chain in the $N \to 0$ limit. We suggest that the fermionic state becomes critical in an anisotropic fashion.