Dynamics of quantum phase transition: exact solution in quantum Ising model

TL;DR

This paper provides an exact solution for the dynamics of a quantum phase transition in the quantum Ising model, revealing how defect density scales with transition rate and connecting it to the Kibble-Zurek mechanism.

Contribution

It offers an exact analytical solution for the quantum Ising model driven through a critical point at finite rate, elucidating defect formation and scaling laws.

Findings

Defect density scales as the square root of the transition rate

Exact solution links quantum dynamics to the Kibble-Zurek mechanism

Quasiparticle excitations follow Landau-Zener level anticrossings

Abstract

Quantum Ising model is an exactly solvable model of quantum phase transition. This paper gives an exact solution when the system is driven through the critical point at finite rate. The evolution goes through a series of Landau-Zener level anticrossings when pairs of quasiparticles with opposite pseudomomenta get excited with probability depending on the transition rate. Average density of defects excited in this way scales like a square root of the transition rate. This scaling is the same as the scaling obtained when the standard Kibble-Zurek mechanism of thermodynamic second order phase transitions is applied to the quantum phase transition in the Ising model.