Crossover to Sachdev-Ye-Kitaev criticality in an infinite-range quantum Heisenberg spin glass

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 N f flavors of spinful fermions. We employ an expansion in N f, which controls the strength of quantum fluctuations, and self-consistently include 1/N f corrections to the Luttinger-Ward functional. In the large- 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 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 χ''(ω) about sgn(ω). At the lowest energies and temperatures, spin glass dynamics ultimately take over, producing a universal sub-Ohmic dynamical spin susceptibility χ''(ω) about sgn(ω) sqrt ω. Our results highlight a direct connection between the suppression of spin-glass order and the emergence of SYK criticality in a frustrated quantum magnet.