Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions

TL;DR

This paper explores universal dynamical scaling in quantum critical spin systems driven out of equilibrium, revealing path-dependent non-ergodic behavior and the impact of multiple level crossings on excitations.

Contribution

It demonstrates that non-equilibrium scaling can be explained by equilibrium exponents but is path-dependent, highlighting non-ergodic scaling in finite-order quantum phase transitions.

Findings

Non-equilibrium scaling relates to equilibrium critical exponents.

Path dependence influences excitation suppression.

Multiple level crossings can prevent excitations.

Abstract

We investigate the emergence of universal dynamical scaling in quantum critical spin systems adiabatically driven out of equilibrium, with emphasis on quench dynamics which involves non-isolated critical points (i.e., critical regions) and cannot be a priori described through standard scaling arguments nor time-dependent perturbative approaches. Comparing to the case of an isolated quantum critical point, we find that non-equilibrium scaling behavior of a large class of physical observables may still be explained in terms of equilibrium critical exponents. However, the latter are in general non-trivially path-dependent, and detailed knowledge about the time-dependent excitation process becomes essential. In particular, we show how multiple level crossings within a gapless phase may completely suppress excitation depending on the control path. Our results typify non-ergodic scaling in continuous finite-order quantum phase transitions.