Evolution of Complexity Following a Global Quench

TL;DR

This paper investigates the time evolution of quantum state complexity after a global quench using the holographic 'complexity equals action' conjecture, finding that the complexity growth rate saturates the conjectured bound shortly after local equilibrium is reached.

Contribution

It applies the holographic complexity equals action conjecture to analyze complexity growth post-quench, demonstrating saturation of the complexity growth bound.

Findings

Complexity growth rate saturates the bound after local equilibrium.

The study supports the conjectured relation between complexity and gravitational action.

Complexity evolution aligns with theoretical bounds shortly after quench.

Abstract

The rate of complexification of a quantum state is conjectured to be bounded from above by the average energy of the state. A different conjecture relates the complexity of a holographic CFT state to the on-shell gravitational action of a certain bulk region. We use 'complexity equals action' conjecture to study the time evolution of the complexity of the CFT state after a global quench. We find that the rate of growth of complexity is not only consistent with the conjectured bound, but it also saturates the bound soon after the system has achieved local equilibrium.