# Quench dynamics and defects formation in the Ising chain in a transverse magnetic field

## TL;DR

This paper investigates the dynamics of the quantum Ising model under time-dependent magnetic fields, extending the Landau-Zener formula to non-adiabatic cases and analyzing defect formation during quenches.

## Contribution

It generalizes the Landau-Zener formula for non-adiabatic evolution and explores defect formation in the Ising chain under various magnetic field protocols.

## Key findings

- Quasi-static fields follow Landau-Zener predictions.
- Shock-wave quenches lead to complex defect patterns.
- Final states depend on pulse amplitude and velocity.

## Abstract

We study analytically and numerically quench dynamics and defects formation in the quantum Ising model in the presence of a time-dependent transverse magnetic field. We generalize the Landau-Ziner formula to the case of non-adiabatic evolution of the quantum system. For a quasi-static magnetic field, with a slow dependence on time, our outcomes are similar to the results predicted by the Landau-Zener formula. However, a quench dynamics under a shock-wave load is more complicated. The final state of the system depends on the amplitude and pulse velocity, resulting in the mixture of ground and excited states and significant density of defects.