The SYK Crossover

The Sachdev-Ye-Kitaev model — random all-to-all coupled fermions — is exactly solvable at large N and displays quantum chaos, non-Fermi liquid behavior, and holographic connections to black holes. But it’s an artificial model: the couplings are chosen to be random and all-to-all by construction. Can SYK-like criticality emerge naturally from a more physical system?

Yes: an infinite-range quantum Heisenberg spin glass crosses over to SYK criticality (arXiv:2603.11263). At large flavor number, the system is a paramagnetic-to-spin-glass transition with temperature independent of N_f. But at intermediate scales, before the spin glass order sets in, both fermionic and spin spectral densities display critical behavior over a broad energy range — SYK-type scale invariance. At lower energies, spin glass dynamics take over with universal sub-Ohmic spin susceptibility.

The structural insight: SYK criticality is not the ground state but the crossover. The system passes through a window of SYK-like behavior on its way to the spin glass phase. The criticality is transient — it dominates an intermediate energy scale where quantum fluctuations are strong but ordering hasn’t yet won. This makes SYK physics experimentally relevant not as a ground state to be stabilized but as a critical regime to be traversed. The crossover is the physics.