Mean Field Theory of a Quantum Heisenberg Spin Glass

A full mean-field solution of a quantum Heisenberg spin-glass model is presented in a large- $N$ limit. A spin-glass transition is found for all values of the spin $S$. The quantum critical regime associated with the quantum transition at $S=0\mathrm{}$ and the various regimes in the spin-glass phase at high spin are analyzed. The specific heat is shown to vanish linearly with temperature. In the spin-glass phase, intriguing connections between the equilibrium properties of the quantum problem and the out-of-equilibrium dynamics of classical models are pointed out.