Do dynamical quantum phase transitions survive at finite temperature?
In plain words
The theory is built for pure starting states at zero temperature. For warm starting states several competing definitions exist, and they disagree on whether the sharp kinks remain.
Precise statement
For an initial Gibbs state $\rho_0 = \exp(-\beta H_i)/Z$, compare generalized Loschmidt echoes (the interferometric echo $\operatorname{tr}(\rho_0 U(t))$ and fidelity-based echoes) in interacting models. Does any measurable generalization show nonanalyticities at finite $\beta$ that connect continuously to the pure-state transitions as $\beta \to \infty$? Answer yes or no, with the definition.
What would settle it
Exact free-fermion results extended to interacting chains by numerics, together with a measurement protocol.
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