# Complexity and scaling in quantum quench in $1+1$ dimensional fermionic field theories

## TL;DR

This paper studies how the complexity of quantum states evolves during a quench in a 1+1 dimensional fermionic field theory, revealing different scaling regimes depending on the quench rate.

## Contribution

It introduces an exactly solvable quench protocol in a relativistic fermion field theory and characterizes the resulting complexity scaling behaviors.

## Key findings

- Saturation of complexity at lattice-scale quenches
- Fast quench scaling behavior observed
- Kibble-Zurek scaling at slow quench rates

## Abstract

We consider the scaling behavior of circuit complexity under quantum quench in an a relativistic fermion field theory on a one dimensional spatial lattice. This is done by finding an exactly solvable quench protocol which asymptotes to massive phases at early and late times and crosses a critical point in between. We find a variety of scaling behavior as a function of the quench rate, starting with a saturation for quenches at the lattice scale, a "fast quench scaling" at intermediate rate and a Kibble Zurek scaling at slow rates.