At finite temperatures, the quantum critical region (QCR) emerges as a consequence of the interplay between thermal and quantum fluctuations. We seek suitable physical quantities, which during dynamics can give prominent response to QCR in the transverse field quantum $XY$ model. We report that the maximum energy absorbed, the nearest neighbor entanglement, and the quantum mutual information of the time-evolved state after a quench of the transverse magnetic field exhibit a faster drop with temperature when the initial magnetic field is taken from within the QCR, compared to the choice of the initial point from different phases. We propose a class of dynamical quantifiers, originating from the response of these physical quantities and show that they can faithfully mimic the equilibrium physics, namely detection of the QCR at finite temperatures.

• Received 27 August 2019
• Revised 22 June 2020
• Accepted 14 July 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033249

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Published by the American Physical Society