The mobility edge problem: Continuous symmetry and a conjecture
Abstract
An apparently overlooked symmetry of the disordered electron problem is derived. It yields the wellknown Wardidentity connecting the one and twoparticle Green's function. This symmetry and the apparent shortrange behaviour of the averaged oneparticle Green's function are used to conjecture that the critical behaviour near the mobility edge coincides with that of interacting matrices which have two different eigenvalues of multiplicity zero (due to replicas). As a consequence the exponent s of the d.c. conductivity is expected to approach 1 for real matrices and 1/2 for complex matrices as the dimensionality of the system approaches two from above. In two dimensions no metallic conductivity is expected.
 Publication:

Zeitschrift fur Physik B Condensed Matter
 Pub Date:
 September 1979
 DOI:
 10.1007/BF01319839
 Bibcode:
 1979ZPhyB..35..207W