Disordered quantum spin chains with long-range antiferromagnetic interactions

We investigate the magnetic susceptibility χ(T) of quantum spin chains of N=1280 spins with power-law long-range antiferromagnetic couplings as a function of their spatial decay exponent α and cutoff length ξ. The calculations are based on the strong disorder renormalization method which is used to obtain the temperature dependence of χ(T) and distribution functions of couplings at each renormalization step. For the case with only algebraic decay (ξ=) we find a crossover at α∗=1.066 between a phase with a divergent low-temperature susceptibility χ(T→0) for α>α∗ to a phase with a vanishing χ(T→0) for α<α∗. For finite cutoff lengths ξ, this crossover occurs at a smaller α∗(ξ). Additionally, we study the localization of spin excitations for ξ=by evaluating the distribution function of excitation energies, and we find a delocalization transition that coincides with the opening of the pseudogap at αc=α∗.