Localization of the electronic states in non-stationary chaotic field with long-range correlation: off-diagonal model

Abstract

The localization problem in stationary and non-stationary chaotic field with long-range correlation, which is generated by modified Bernoulli map, is numerically studied. The map can generate stationary ( B<2) and non-stationary ( B⩾2) sequence by changing the parameter B. We investigate effect of the correlation on the localization in the electronic states of the off-diagonal model by Lyapunov exponent γ (inverse localization length) and localization length ξ in the stationary and non-stationary regime. At the band center ( E=0) the localization length diverges as ξ∼| E| −2 independently of B. It is also numerically shown that the B-dependence of the Lyapunov exponent obeys, γ∝− B for B⩽2, and exponentially decreases for B>2. Furthermore, we investigate the system size N-dependence of the localization length. It is confirmed that even in the strongly correlated cases ( B⩽3.0) the exponential localization is remained, i.e., ξ∼ N ν ( ν∼0), in the thermodynamic limit, except for the band center energy.