Spin liquid to spin glass crossover in the random quantum Heisenberg magnet

We study quantum SU(M) spins with all-to-all and random Heisenberg exchange interactions of root-mean square strength J. The M -> infinity model has a quantum spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with S = 1/2 spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a 1/M expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order q(EA). The SYK spin liquid behavior persists down to a frequency omega(*) similar to J(qEA), and for omega < omega(*), the spin spectral density is linear in omega, thus quenching the extensive zero temperature entropy of the spin liquid. The linear CO spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large q(EA). We argue that the extensive SYK spin liquid entropy is transformed as T -> 0 to an extensive complexity of the spin glass state. We comment on holographic connections of the confinement transition to the fragmentation of black holes with AdS(2) horizons.