Dynamical response of quantum spin-glass models at T=0

We study the behavior of two archetypal quantum spin glasses at T = 0 by exact diagonalization techniques: the random Ising model in a transverse field and the random Heisenberg model. The behavior of the dynamical spin response is obtained in the spin-glass ordered phase. In both models it is gapless and has the general form chi"(omega) = q delta(omega) + chi (reg)"(omega), with chi (reg)"(omega) similar to omega for the Ising and chi (reg)"(omega) similar to const for the Heisenberg. at low frequencies. The method provides new insight to the physical nature of the low-lying excitations.