A clean local lattice model with SYK low-energy physics
In plain words
SYK needs random couplings among all particles, which no real material has. It is unknown whether an ordinary non-random lattice with short-range interactions can behave the same way at low temperature.
Precise statement
Find a translation-invariant lattice Hamiltonian with finite-range interactions and no quenched disorder whose low-temperature regime shows SYK signatures: fermion Green function $G(\tau) \sim \tau^{-1/2}$ over a parametrically wide window, a large residual entropy density before a crossover scale, and Lyapunov exponent approaching $2 \pi k_{B} T/\hbar$. Answer: an explicit model with controlled evidence, or an argument that none exists.
What would settle it
Controlled numerics or an exact solution demonstrating these three signatures in a specific clean model.
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