# Adiabatic dynamics of quasiperiodic transverse Ising model

## TL;DR

This paper investigates the non-equilibrium dynamics of a quasiperiodic transverse Ising model crossing its quantum critical point, confirming Kibble-Zurek scaling with predicted exponents for defect density.

## Contribution

It demonstrates the validity of Kibble-Zurek scaling in a quasiperiodic system with multiple critical lines belonging to different universality classes.

## Key findings

- Power-law scaling of defect density confirmed.
- Exponents match Kibble-Zurek predictions.
- Scaling holds across different critical lines.

## Abstract

We study the non-equilibrium dynamics due to slowly taking a quasiperiodic Hamiltonian across its quantum critical point. The special quasiperiodic Hamiltonian that we study here has two different types of critical lines belonging to two different universality classes, one of them being the well known quantum Ising universality class. In this paper, we verify the Kibble Zurek scaling which predicts a power law scaling of the density of defects generated as a function of the rate of variation of the Hamiltonian. The exponent of this power law is related to the equilibrium critical exponents associated with the critical point crossed. We show that the power-law behavior is indeed obeyed when the two types of critical lines are crossed, with the exponents that are correctly predicted by Kibble Zurek scaling.