Subsystem complexity after a global quantum quench

TL;DR

This paper investigates how the complexity of a subsystem in harmonic lattices evolves over time after a global quantum quench, using Fisher information geometry and comparing it with entanglement entropy.

Contribution

It introduces a method to evaluate subsystem complexity via Fisher information geometry and analyzes its temporal evolution post-quench, including bounds and asymptotic behavior.

Findings

Subsystem complexity exhibits distinct temporal dynamics compared to entanglement entropy.

Upper and lower bounds for the complexity evolution are derived.

Asymptotic complexity is characterized using the generalized Gibbs ensemble.

Abstract

We study the temporal evolution of the circuit complexity for a subsystem in harmonic lattices after a global quantum quench of the mass parameter, choosing the initial reduced density matrix as the reference state. Upper and lower bounds are derived for the temporal evolution of the complexity for the entire system. The subsystem complexity is evaluated by employing the Fisher information geometry for the covariance matrices. We discuss numerical results for the temporal evolutions of the subsystem complexity for a block of consecutive sites in harmonic chains with either periodic or Dirichlet boundary conditions, comparing them with the temporal evolutions of the entanglement entropy. For infinite harmonic chains, the asymptotic value of the subsystem complexity is studied through the generalised Gibbs ensemble.