Subsystem complexity after a local quantum quench

TL;DR

This paper investigates how the circuit complexity evolves over time after a local quantum quench in harmonic chains, revealing behaviors like revivals and logarithmic growth, with the dynamics depending on the subsystem's position relative to the quench point.

Contribution

It introduces a numerical approach using Fisher information geometry to analyze subsystem complexity evolution after a local quench in harmonic chains, highlighting the impact of the joining point's location.

Findings

Subsystem complexity exhibits revivals and logarithmic growth.

The behavior depends on whether the joining point is inside or outside the subsystem.

Complexity evolution parallels entanglement entropy when the joining point is outside the subsystem.

Abstract

We study the temporal evolution of the circuit complexity after the local quench where two harmonic chains are suddenly joined, choosing the initial state as the reference state. We discuss numerical results for the complexity for the entire chain and the subsystem complexity for a block of consecutive sites, obtained by exploiting the Fisher information geometry of the covariance matrices. The qualitative behaviour of the temporal evolutions of the subsystem complexity depends on whether the joining point is inside the subsystem. The revivals and a logarithmic growth observed during these temporal evolutions are discussed. When the joining point is outside the subsystem, the temporal evolutions of the subsystem complexity and of the corresponding entanglement entropy are qualitatively similar.