A central question in frustrated quantum magnets is how quantum fluctuations destabilize spin-glass order and promote quantum spin-liquid behavior. We study the equilibrium dynamics of an infinite-range quantum Heisenberg model with random couplings, in which local magnetic moments arise from ${\mathcal{N}}_f$ flavors of spinful fermions. We employ an expansion in ${\mathcal{N}}_f$, which controls the strength of quantum fluctuations, and self-consistently include $1/{\mathcal{N}}_f$ corrections to the Luttinger-Ward functional. In the large-${\mathcal{N}}_f$ limit, where quantum fluctuations are weak, the high- and low-temperature phases are respectively paramagnetic and spin glass ordered, with a transition temperature independent of ${\mathcal{N}}_f$. For small numbers of fermionic flavors, however, quantum fluctuations substantially suppress the ordering temperature. We show that this behavior reflects the proximity of the system to a Sachdev-Ye-Kitaev (SYK) regime, realizing quantum spin-liquid dynamics over a broad range of finite frequencies, where both fermionic and spin spectral densities display critical behavior over a broad range of finite frequencies, with the latter exhibiting the scale-invariant form ${\chi }^{\prime \prime }(\omega )\sim \mathrm{sgn}(\omega )$. At the lowest energies and temperatures, spin glass dynamics ultimately take over, producing a universal sub-Ohmic dynamical spin susceptibility ${\chi }^{\prime \prime }(\omega )\sim \mathrm{sgn}(\omega )\sqrt{|\omega |}$. Our results highlight a direct connection between the suppression of spin-glass order and the emergence of SYK criticality in a frustrated quantum magnet.

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• Quantum criticality
• Quantum phase transitions
• Strongly correlated systems
• Sachdev-Ye-Kitaev model