# The Kibble-Zurek mechanism at exceptional points

## TL;DR

This paper extends the Kibble-Zurek mechanism to non-Hermitian systems at exceptional points, revealing how defect density scales during finite-rate parameter ramps and demonstrating defect suppression due to decay near EPs.

## Contribution

It generalizes the Kibble-Zurek mechanism to exceptional points in non-Hermitian systems, providing a new scaling law and physical interpretation via Lindblad dynamics.

## Key findings

- Defect density scales as τ^{-(d+z)ν/(zν+1)} during ramps across EPs.
- Adiabatic evolution leads to eigenstates of the final non-Hermitian Hamiltonian.
- Defect production is suppressed compared to Hermitian systems due to decay near EPs.

## Abstract

Exceptional points (EPs) are ubiquitous in non-hermitian systems, and represent the complex counterpart of critical points. By driving a system through a critical point at finite rate induces defects, described by the Kibble-Zurek mechanism, which finds applications in diverse fields of physics. Here we generalize this to a ramp across an EP. We find that adiabatic time evolution brings the system into an eigenstate of the final non-hermitian Hamiltonian and demonstrate that for a variety of drives through an EP, the defect density scales as $\tau^{-(d+z)\nu/(z\nu+1)}$ in terms of the usual critical exponents and $1/\tau$ the speed of the drive. Defect production is suppressed compared to the conventional hermitian case as the defect state can decay back to the ground state close to the EP. We provide a physical picture for the studied dynamics through a mapping onto a Lindblad master equation with an additionally imposed continuous measurement.