title: Dynamics of a quantum phase transition: exact solution of the quantum Ising model.
abstract: The Quantum Ising model is an exactly solvable model of quantum phase transition. This Letter gives an exact solution when the system is driven through the critical point at a finite rate. The evolution goes through a series of Landau-Zener level anticrossings when pairs of quasiparticles with opposite pseudomomenta get excited with a probability depending on the transition rate. The 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.
authors.affiliation: Institute of Physics and Centre for Complex Systems, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland.
authors.forename: Jacek
authors.initials: J
authors.lastname: Dziarmaga