Quantum phase transition dynamics in the two-dimensional transverse-field Ising model
June 18, 2021
Markus Schmitt, Marek M. Rams, Jacek Dziarmaga, Markus Heyl, and Wojciech H. Zurek

The quantum Kibble-Zurek mechanism (QKZM) predicts universal dynamical
behavior in the vicinity of quantum phase transitions (QPTs). It is now well
understood for one-dimensional quantum matter. Higher-dimensional systems,
however, remain a challenge, complicated by fundamental differences of the
associated QPTs and their underlying conformal field theories. In this work, we
take the first steps towards exploring the QKZM in two dimensions. We study the
dynamical crossing of the QPT in the paradigmatic Ising model by a joint effort
of modern state-of-the-art numerical methods. As a central result, we quantify
universal QKZM behavior close to the QPT. However, upon traversing further into
the ferromagnetic regime, we observe deviations from the QKZM prediction. We
explain the observed behavior by proposing an {\it extended QKZM} taking into
account spectral information as well as phase ordering. Our work provides a
starting point towards the exploration of dynamical universality in
higher-dimensional quantum matter.
arXiv:2106.09046