Thermal critical dynamics from equilibrium quantum fluctuations

TL;DR

This paper demonstrates that quantum fluctuations exhibit a singularity at thermal critical points, enabling the extraction of the dynamical critical exponent directly from static quantum fluctuations without classical modeling.

Contribution

It introduces a method to determine the dynamical $z$ exponent from static quantum fluctuations at thermal critical points, bypassing classical effective models.

Findings

Quantum fluctuations show a singularity at thermal critical points.

The dynamical $z$ exponent can be extracted from static quantities.

Static and dynamic properties remain linked in quantum systems at finite temperature.

Abstract

We show that quantum fluctuations display a singularity at thermal critical points, involving the dynamical $z$ exponent. Quantum fluctuations, captured by the quantum variance (I. Fr\'erot and T. Roscilde, 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.