Non-equilibrium dynamic critical scaling of the quantum Ising chain

TL;DR

This paper derives the finite-size scaling functions for the quantum Ising chain during a dynamic ramp through criticality and demonstrates the universality of these features in related experimental systems, revealing novel athermal behaviors.

Contribution

It provides the first explicit solution for the time-dependent scaling functions during a non-equilibrium ramp in the quantum Ising chain and confirms universality in experimental analogs.

Findings

Scaling functions exhibit qualitatively athermal features

Negative spin correlations are predicted and observable

Universality extends to experimentally studied systems

Abstract

We solve for the time-dependent finite-size scaling functions of the 1D transverse-field Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally-studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and show that they should be robustly observable within present cold atom experiments.