Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model

Dziarmaga, Jacek

doi:10.1103/PhysRevLett.95.245701

Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model

Jacek Dziarmaga

Dec 9, 2005

Published in:

Phys.Rev.Lett. 95 (2005) 24, 245701

Published: Dec 9, 2005

DOI:

10.1103/PhysRevLett.95.245701

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Abstract: (APS)

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.

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