We describe the interplay of quantum and thermal fluctuations in the infinite-range Heisenberg spin glass. This model is generalized to $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ symmetry, and we describe the phase diagram as a function of the spin S and 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, ${\chi }_{\mathrm{loc}}^{″}\left(\omega \right)\sim \omega$ 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 with ${\chi }_{\mathrm{loc}}^{″}\sim \tanh (\omega /2T)$ dominates the properties over a significant range of T and ω. We argue that the latter state may be relevant in understanding the properties of strongly disordered transition-metal and rare-earth compounds.

• Received 25 September 2000

DOI:https://doi.org/10.1103/PhysRevB.63.134406