When dynamical transitions coincide with equilibrium criticality or order · revision history

Revision 2

Accepted · core change · record

Changes against revision 1:

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 · changed · core
Revision 1: 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.
Revision 2: For a quench $H_i \to H_f$, the Loschmidt rate $l(t) = -\lim_{N \to \infty} (1/N) \ln \mid\langle\psi_0\mid \exp(-i H_f t/\hbar) \mid\psi_0\rangle\mid^2$ 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

Decisions