We show that quantum fluctuations display a singularity at thermal critical points, involving the dynamical $z$ exponent. Quantum fluctuations, captured by the quantum variance [Frérot et al., Phys. Rev. B 94, 075121 (2016)], can be expressed via purely static quantities; this in turn allows us to extract the $z$ exponent related to the intrinsic Hamiltonian dynamics via equilibrium unbiased numerical calculations, without invoking any effective classical model for the critical dynamics. These findings illustrate that, unlike classical systems, in quantum systems static and dynamic properties remain inextricably linked even at finite-temperature transitions, provided that one focuses on static quantities that do not bear any classical analog—namely, on quantum fluctuations.

• Received 8 November 2021
• Revised 1 February 2022
• Accepted 1 March 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.130601

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society