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 Group (SDRG) 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 pseudo-gap opening at α_c = α*.

Currently we are working on the corrections necessary to obtain an α and ξ dependence on the concurrence between two spin, which is inexistent in the standard SDRG framework.