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 large M model has a 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 ω_s ∼ Jq_EA, and for ω < ω_s, the spectral density is linear in ω, thus quenching the extensive zero temperature entropy of the spin liquid. The linear ω 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.