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We present the mean field solution of the quantum and classical Heisenbergspin glasses, using the combination of a high precision numerical solution ofthe Parisi full replica symmetry breaking equations and a continuous timeQuantum Monte Carlo. We characterize the spin glass order and its low-energyexcitations down to zero temperature. The Heisenberg spin glass has a rougherenergy landscape than its Ising analogue, and exhibits a very slow temperatureevolution of its dynamical properties. We extend our analysis to the doped,metallic Heisenberg spin glass, which displays an unexpectedly slow spindynamics reflecting the proximity to the melting quantum critical point and itsassociated Sachdev-Ye-Kitaev Planckian dynamics.

Exact numerical solution of the classical and quantum Heisenberg spin glass