The infinite-range quantum random Heisenberg magnet

We study with exact diagonalization techniques the Heisenberg model for a system of SU(2) spins with S=1/2 and random infinite-range exchange interactions. We calculate the critical temperature T_g for the spin-glass to paramagnetic transition. We obtain T_g ~ 0.13, in good agreement with previous quantum Monte Carlo and analytical estimates. We provide a detailed picture for the different kind of excitations which intervene in the dynamical response chi''(w,T) at T=0 and analyze their evolution as T increases. We also calculate the specific heat Cv(T). We find that it displays a smooth maximum at TM ~ 0.25, in good qualitative agreement with experiments. We argue that the fact that TM>Tg is due to a quantum disorder effect.