Complexity as a novel probe of quantum quenches: universal scalings and purifications

TL;DR

This paper explores how quantum complexity behaves during quenches in 1+1 dimensions, revealing universal scaling laws and its ability to detect features beyond entanglement entropy, with implications for holography.

Contribution

It introduces the application of quantum complexity to quantum quenches, demonstrating universal scalings and the complexity of purification in free field theories.

Findings

Complexity exhibits universal scalings in slow and fast quenches.

Complexity of purification can detect features beyond entanglement entropy.

Subregion complexity is subadditive, with potential holographic implications.

Abstract

We apply the recently developed notion of complexity for field theory to a quantum quench through a critical point in 1+1 dimensions. We begin with a toy model consisting of a quantum harmonic oscillator, and show that complexity exhibits universal scalings in both the slow and fast quench regimes. We then generalize our results to a 1-dimensional harmonic chain, and show that preservation of these scaling behaviours in free field theory depends on the choice of norm. Applying our set-up to the case of two oscillators, we quantify the complexity of purification associated to a subregion, and demonstrate that complexity is capable of probing features to which the entanglement entropy is insensitive. We find that the complexity of subregions is subadditive, and comment on potential implications for holography.