Thermal Critical Dynamics from Equilibrium Quantum Fluctuations

We show that quantum fluctuations display a singularity at thermal critical points, involving the dynamical z exponent. Quantum fluctuations, captured by the quantum variance [Frerot 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 hear any classical analog-namely, on quantum fluctuations.

Automated summary

We demonstrate the singularity of quantum fluctuations at thermal critical points and its connection to the dynamical z exponent. By expressing the quantum fluctuations in terms of purely static quantities, we extract the z exponent related to the intrinsic Hamiltonian dynamics through unbiased numerical calculations, without the need for an effective classical model. These findings highlight the inseparable link between static and dynamic properties in quantum systems, which is different from classical systems, even at finite-temperature transitions.