Disordered quantum spin chains with long-range antiferromagnetic interactions

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