Fluctuations in a Quantum Random Heisenberg Paramagnet

We solve the $S=1\mathrm{}/2$ infinite-range random Heisenberg Hamiltonian in the paramagnetic phase using quantum Monte Carlo and analytical techniques. We find that the spin-glass susceptibility diverges at a finite temperature $T_g$ which demonstrates the existence of a low-temperature ordered phase. Quantum fluctuations reduce the critical temperature and the effective Curie constant with respect to their classical values. They also give rise to a redistribution of spectral weight in the dynamic structure factor in the paramagnetic phase. As the temperature decreases the spectrum of magnetic excitations gradually splits into quasielastic and inelastic contributions whose weights scale as $S^2$ and $S$ at low temperature.