UNUSUAL PROPERTIES OF MIDBAND STATES IN SYSTEMS WITH OFF-DIAGONAL DISORDER

It is known that off-diagonal disorder results in anomalous localizati on at the band center, whereas diagonal disorder does not. We show tha t the important distinction is riot between diagonal and off-diagonal disorder, but between bipartite and nonbipartite lattices. We prove th at bipartite lattices in any dimension (and some generalizations that are not bipartite) have zero energy (i.e., band-center) eigenfunctions that vanish on one sublattice. We show that ln\psi(j)\ has random-wal k behavior for one-dimensional systems with first-, or first- and thir d-neighbor random hopping, leading to exp(-lambda root r) localization of the zero-energy eigenfunction. Addition of diagonal disorder leads to a biased random walk. First- and second-neighbor random hopping wi th no diagonal disorder leads to ordinary exponential [exp(lambda tau) ] localization. Numerical simulations show anomalous localization in d imensions 1 and 2, with additional periodic structure in some cases.