Quantum fluctuations of a nearly critical Heisenberg spin glass

Abstract

We describe the interplay of quantum and thermal fluctuations in the infinite-range Heisenberg spin glass. This model is generalized to $\mathrm{SU}(N)$ 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, ${\ensuremath{\chi}}_{\mathrm{loc}}^{\ensuremath{''}}(\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\omega}$ 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 ${\ensuremath{\chi}}_{\mathrm{loc}}^{\ensuremath{''}}\ensuremath{\sim}\mathrm{tanh}(\ensuremath{\omega}/2T)$ dominates the properties over a significant range of T and \ensuremath{\omega}. We argue that the latter state may be relevant in understanding the properties of strongly disordered transition-metal and rare-earth compounds.