Transitions in locally interacting systems

Determine whether phase transitions analogous to the first-order MRE transition found in the Sachdev–Ye–Kitaev model occur in systems with spatially local interactions, and characterize how the growth of the magic Rényi entropy depends on transport and scrambling.

Background

The paper identifies a first-order transition in the MRE density of a Kourkoulou–Maldacena state evolving under the all-to-all interacting Sachdev–Ye–Kitaev Hamiltonian. The authors leave unresolved whether comparable collective behavior survives when interactions are spatially local, where transport and scrambling provide additional dynamical constraints. This problem seeks to establish the relevance and universality of the observed transition beyond the SYK setting.