Dynamics of a quantum phase transition in the random Ising model

TL;DR

This paper investigates the non-adiabatic dynamics of a quantum phase transition in the random Ising model, revealing a logarithmic dependence of defect density on transition rate, contrasting with power-law predictions for pure systems.

Contribution

It demonstrates that disorder in the random Ising model leads to a fundamentally different defect scaling behavior during quantum phase transitions.

Findings

Defect density depends logarithmically on transition rate.

Transition dynamics are non-adiabatic at all rates.

Disorder alters the scaling laws predicted by Kibble-Zurek mechanism.

Abstract

A quantum phase transition from paramagnetic to ferromagnetic phase is driven by a time-dependent external magnetic field. For any rate of the transition the evolution is non-adiabatic and finite density of defects is excited in the ferromagnetic state. The density of excitations has only logarithmic dependence on the transition rate. This is much weaker than any usual power law scaling predicted for pure systems by the Kibble-Zurek mechanism.