Holographic local quench and effective complexity

TL;DR

This paper investigates how holographic complexity evolves after a local quench in 1+1D conformal field theories, comparing CV and CA conjectures, and explores their relation to entanglement measures and computational bounds.

Contribution

It provides a detailed analysis of holographic complexity dynamics post-quench and discusses their significance as measures of effective complexity, highlighting non-trivial features.

Findings

Complexity evolution shows non-trivial features indicating physical relevance.

Lloyd bound is saturated in certain regimes.

Holographic complexities capture key properties of effective complexity.

Abstract

We study the evolution of holographic complexity of pure and mixed states in $1+1$-dimensional conformal field theory following a local quench using both the "complexity equals volume" (CV) and the "complexity equals action" (CA) conjectures. We compare the complexity evolution to the evolution of entanglement entropy and entanglement density, discuss the Lloyd computational bound and demonstrate its saturation in certain regimes. We argue that the conjectured holographic complexities exhibit some non-trivial features indicating that they capture important properties of what is expected to be effective (or physical) complexity.