When dynamical transitions coincide with equilibrium criticality or order
In plain words
The kinks in the return probability were first linked to crossing an ordinary phase transition, but counterexamples exist in both directions. A general rule for when they match is missing.
Precise statement
For a quench $H_i \to H_f$, the Loschmidt rate $l(t) = -\operatorname{lim}_{N \to \infty} (1/N) \operatorname{ln} \mid\langle\psi_0\mid \operatorname{exp}(-i H_f t/\hbar) \mid\psi_0\rangle\mid^2$ can be nonanalytic at critical times $t_c$. Determine conditions on $(H_i, H_f)$ under which (a) such $t_c$ exist if and only if the quench crosses an equilibrium critical point and (b) $t_c$ coincide with zeros or sign changes of the order parameter. Answer: a classification valid beyond free-fermion models.
What would settle it
A general criterion proved or verified across interacting nonintegrable models in $d = 1 \text{ and } 2$.
Status in the literature
Counterexamples in both directions are known since 2014; no general criterion exists.
Related problems
- More general than Do dynamical transitions occur only for quenches across critical points
- More general than Do dynamical transition times coincide with zeros of the order parameter