Mobility edges and critical exponents in the disordered double chains with long-range correlation

In this paper, we investigate the localization-delocalization transitions of two types of disordered double chain models with long-range correlation. Based on the empirical methods, we find the exact positions of the two pairs of mobility edges between the localized states and the extended states, which are perfectly in agreement with the numerical results obtained by the transfer matrix method. In the case with interchain correlation in on-site energy (a linear relationship between the corresponding site energies of the two chains), a second-order quantum phase transition has been identified, which is manifested as the jump of critical exponent of the localization length. While for the case without interchain correlation in on-site energy, i.e., the disordered on-site energies of the two chains are independently, the critical exponent is determined by one of the two chains, of which the degree of long-range correlation is smaller.