Universality of thermodynamics and chaos in arbitrary combinations of large‑q SYK models

Determine whether the robustness of SYK universality—specifically the preservation of phase diagram topology, mean‑field critical exponents, and maximal chaos—extends from two‑term perturbations such as J_q H_q + J_{q/2} H_{q/2} to arbitrary finite sums of large‑q SYK Hamiltonians H = ∑_κ J_{κ q} H_{κ q}, where each H_{κ q} is a κq/2‑body all‑to‑all interaction in the large‑q limit. Establish precise conditions under which these universal thermodynamic and chaotic properties persist for general combinations of interaction scales.

Background

Within the discussion of quantum chaos and thermodynamics, the authors show that SYK models exhibit a robust set of universal features: a first‑order line ending at a critical point characterized by Landau‑Ginzburg exponents, and maximal quantum chaos saturating the MSS bound at low temperatures. They note that adding specific additional interaction scales (e.g., combining q‑ and q/2‑body terms) preserves these universal properties and phase diagram topology.

This motivates the broader question of whether such robustness holds for arbitrary linear combinations of large‑q SYK Hamiltonians with multiple interaction scales, rather than only for particular two‑term perturbations already studied. Confirming or refuting this would clarify the scope of SYK universality across a more general class of strongly interacting models.