Dynamics of longitudinal magnetization in transverse-field quantum Ising model: from symmetry-breaking gap to Kibble-Zurek mechanism

TL;DR

This paper investigates how the symmetry-breaking gap in the quantum Ising model can be determined from the dynamics of longitudinal magnetization after a magnetic field quench, linking it to the Kibble-Zurek mechanism.

Contribution

It demonstrates a method to extract the symmetry-breaking gap from magnetization dynamics and validates the approach with numerical simulations aligned with Kibble-Zurek theory.

Findings

Magnetization evolution reveals the symmetry-breaking gap.

Simulation results agree with Kibble-Zurek predictions.

Method applicable to cold atom, ion experiments, and quantum annealers.

Abstract

We show that the symmetry-breaking gap of the quantum Ising model in the transverse field can be extracted from free evolution of the longitudinal magnetization taking place after a gradual quench of the magnetic field. We perform for this purpose numerical simulations of the Ising chains with either periodic or open boundaries. We also study the condition for adiabaticity of evolution of the longitudinal magnetization finding excellent agreement between our simulations and the prediction based on the Kibble-Zurek theory of non-equilibrium phase transitions. Our results should be relevant for ongoing cold atom and ion experiments targeting either equilibrium or dynamical aspects of quantum phase transitions. They could be also useful for benchmarking D-Wave machines.