Evolution of circuit complexity in a harmonic chain under multiple quenches

TL;DR

This paper investigates how circuit complexity evolves in a harmonic chain subjected to multiple quenches, revealing unique behaviors such as a non-zero lower limit after quenches and the ability to reach high complexity through successive quenches.

Contribution

It introduces the study of Nielsen's circuit complexity under multiple quenches in a harmonic chain, highlighting behaviors not seen in other information measures.

Findings

Complexity shows a non-zero lower limit after two quenches.

Multiple quenches can increase complexity beyond single quench limits.

Crossover phenomena occur between complexities of different quenches.

Abstract

We study Nielsen's circuit complexity in a periodic harmonic oscillator chain, under single and multiple quenches. In a multiple quench scenario, it is shown that the complexity shows remarkably different behaviour compared to the other information theoretic measures, such as the entanglement entropy. In particular, after two successive quenches, when the frequency returns to its initial value, there is a lower limit of complexity, which cannot be made to approach zero. Further, we show that by applying a large number of successive quenches, the complexity of the time evolved state can be increased to a high value, which is not possible by applying a single quench. This model also exhibits the interesting phenomenon of crossover of complexities between two successive quenches performed at different times.