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 coupling 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= \infty$) we find a crossover at $α^*=1.066$ between a phase with a divergent low-temperature susceptibility $χ(T\rightarrow 0) $ for $α> α^*$ to a phase with a vanishing $χ(T\rightarrow 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= \infty$ by evaluating the distribution function of excitation energies and we find a delocalization transition that coincides with the opening of the pseudo-gap at $α_c=α^*$.