Can a local measurement detect a dynamical transition in large systems?
In plain words
The return probability shrinks exponentially with system size, so it cannot be measured in big systems. The question is whether some quantity measured on a few sites shows the same sharp kinks.
Precise statement
For interacting lattice systems with $N\to \infty$, is there a local or few-body observable, or a measurable distribution such as the full counting statistics of the order parameter, whose time dependence is nonanalytic exactly at the DQPT times $t_c$? Answer yes or no, with a construction.
What would settle it
A proof or explicit construction in an interacting nonintegrable model, demonstrated in a quantum simulator with more than about 50 sites.
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