A quantum phase transition is generally thought to imprint distinctive characteristics on the nonequilibrium dynamics of a closed quantum system. Specifically, the Loschmidt echo after a sudden quench to a quantum critical point-measuring the time dependence of the overlap between initial and time-evolved states-is expected to exhibit an accelerated relaxation followed by periodic revivals. We here introduce a new exactly solvable model, the extended Su-Schrieffer-Heeger model, the Loschmidt echo of which provides a counterexample. A parallell analysis of the quench dynamics of the three-site spin-interacting XY model allows us to pinpoint the conditions under which a periodic Loschmidt revival actually appears.
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