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Title: When dynamical transitions coincide with equilibrium criticality or order
Plain: 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: 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.
Settled by: A general criterion proved or verified across interacting nonintegrable models in $d = 1 \text{ and } 2$.
Kind: well-posed
Answer type: classification
References: (empty)
Literature status: partially-resolved
Status note: Counterexamples in both directions are known since 2014; no general criterion exists.
Posed since: 2013