Low-energy fixed points of random quantum spin chains

The one-dimensional isotropic quantum Heisenberg spin systems with random couplings and random spin sizes are investigated using a real-space renormalization-group scheme. It is demonstrated that these systems belong to a universality class of disordered spin systems, characterized by weakly coupled large effective spins. In this large-spin phase the uniform magnetic susceptibility diverges as ${\mathrm{T}}^{\mathrm{-}1}$ with a nonuniversal Curie constant at low temperatures T, while the specific heat vanishes as ${\mathrm{T}}^{\mathrm{|}\mathrm{\alpha }\mathrm{|}}$|ln T| for T→0. For a broad range of initial distributions of couplings and spin sizes the distribution functions approach a single fixed-point form, where α≈-0.44. For some singular initial distributions, however, the fixed-point form of distributions becomes nonuniversal, suggesting that there is a line of fixed points.