  We describe the interplay of quantum and thermal fluctuations in the
infinite-range Heisenberg spin glass. This model is generalized to SU(N)
symmetry, and we describe the phase diagram as a function of the spin S and the
temperature T. The model is solved in the large N limit and certain universal
critical properties are shown to hold to all orders in 1/N. For large S, the
ground state is a spin glass, but quantum effects are crucial in determining
the low T thermodynamics: we find a specific heat linear in T and a local
spectral density of spin excitations linear in frequency for a spin glass state
which is marginally stable to fluctuations in the replicon modes. For small S,
the spin-glass order is fragile, and a spin-liquid state dominates the
properties over a significant range of temperatures and frequencies. We argue
that the latter state may be relevant in understanding the properties of
strongly-disordered transition metal and rare earth compounds.
