Complexity and Floquet dynamics: non-equilibrium Ising phase transitions

TL;DR

This paper investigates the time-dependent circuit complexity of a periodically driven transverse field Ising model, revealing how complexity signals non-equilibrium phase transitions and exhibits universal behaviors at critical points.

Contribution

It analytically computes complexity in Floquet systems, demonstrating its ability to distinguish phases and identify critical points through universal and non-analytic features.

Findings

Complexity shows linear behavior at early times in different phases.

Complexity exhibits non-analytic behavior at phase transition points.

Time-averaged complexity can signal non-equilibrium phase transitions.

Abstract

We study the time-dependent circuit complexity of the periodically driven transverse field Ising model using Nielsen's geometric approach. In the high-frequency driving limit the system is known to exhibit non-equilibrium phase transitions governed by the amplitude of the driving field. We analytically compute the complexity in this regime and show that it clearly distinguishes between the different phases, exhibiting a universal linear behavior at early times. We also evaluate the time averaged complexity, provide evidence of non-analytic behavior at the critical points, and discuss its origin. Finally, we comment on the freezing of quantum dynamics at specific configurations and on the use of complexity as a new tool to understand quantum phase transitions in Floquet systems.