Ground State of the S=1/2 Heisenberg Spin Chain with Random Ferromagnetic and Antiferromagnetic Couplings

We study the Heisenberg $S=1/2$ chain with random ferro- and antiferromagnetic couplings using quantum Monte Carlo simulations at ultra-low temperatures, converging to the ground state. Finite-size scaling of correlation functions and excitation gaps demonstrate an exotic critical state in qualitative agreement with previous strong-disorder renormalization group calculations but with scaling exponents depending on the coupling distribution. We find dual scaling regimes of the transverse correlations versus the distance, with an $L$ independent form $C(r)={r}^{\ensuremath{-}\ensuremath{\mu}}$ for $r\ensuremath{\ll}L$ and $C(r,L)={L}^{\ensuremath{-}\ensuremath{\eta}}f(r/L)$ for $r/L>0$, where $\ensuremath{\mu}>\ensuremath{\eta}$ and the scaling function is delivered by our analysis. These results are at variance with previous spin-wave and density-matrix renormalization group calculations, thus highlighting the power of unbiased quantum Monte Carlo simulations.