Exact results for spatial decay of correlations in low-dimensional insulators II

We study decay rates of one-body reduced density matrices in insulators, described by a tight-binding model, where not only an external potential but also hoppings are spatially modulated. We determine analytically the power in the power law and the correlation length in D=1 case and in several lattice directions in D=2 case. Unlike the uniform hopping case, in D=1 system and in some directions of D=2 system the correlation length is not determined uniquely by the gap. Moreover, a crossover from D=2-decay rates to D=1 ones is investigated.