Long-Range Quantum Ising Spin Glasses at T=0: Gapless Collective Excitations and Universality

We solve the Sherrington-Kirkpatrick model in a transverse field Gamma deep in its quantum glass phase at zero temperature. We show that the glass phase is critical everywhere, exhibiting collective excitations with a gapless Ohmic spectral function. Using an effective potential approach, we interpret the latter as arising from disordered collective excitations behaving like weakly coupled, underdamped oscillators. For a small transverse field Gamma, the low-frequency spectrum takes a form independent of the fluctuation strength Gamma.