Universal scaling near dynamical transitions in interacting systems
In plain words
Ordinary phase transitions have universal exponents shared by very different materials. Whether the kinks in the return probability have universal exponents in interacting two- and three-dimensional systems is not known.
Precise statement
Near $t_c$, determine whether $\ell(t)-\ell(t_c)\sim \left|t-t_c\right|^a$ with exponent a independent of microscopic details for interacting models in $d=2,3$ (e.g. the transverse-field Ising model quenched from the paramagnet deep into the ferromagnet). Answer: values of a and their classification.
What would settle it
Large-scale 2D numerics (tensor networks or neural quantum states) plus a renormalization-group theory predicting the exponents.
Status in the literature
Heyl (2015) derived universal scaling for a class of Ising-type quenches; generic interacting cases remain open.