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Quenching dynamics of a quantum XY spin-$1/2$ chain in a transverse field

Mukherjee, Victor and Divakaran, Uma and Dutta, Amit and Sen, Diptiman (2007) Quenching dynamics of a quantum XY spin-$1/2$ chain in a transverse field. In: Physical Review B, 76 . 174303-1-174303-8.

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Abstract

We study the quantum dynamics of a one-dimensional spin-$1/2$ anisotropic XY model in a transverse field when the transverse field or the anisotropic interaction is quenched at a slow but uniform rate. The two quenching schemes are called transverse and anisotropic quenching, respectively. Our emphasis in this paper is on the anisotropic quenching scheme, and we compare the results with those of the other scheme. In the process of anisotropic quenching, the system crosses all the quantum critical lines of the phase diagram where the relaxation time diverges. The evolution is nonadiabatic in the time interval when the parameters are close to their critical values, and is adiabatic otherwise. The density of defects produced due to nonadiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as $1/\sqrt{\tau}$, where \tau is the characteristic time scale of quenching, a scenario that supports the Kibble-Zurek mechanism. Interestingly, in the case of anisotropic quenching, there exists an additional nonadiabatic transition, in comparison to the transverse quenching case, with the corresponding probability peaking at an incommensurate value of the wave vector. In the special case in which the system passes through a multicritical point, the defect density is found to vary as $1/ \tau^{1/6}$. The von Neumann entropy of the final state is shown to maximize at a quenching rate around which the ordering of the final state changes from antiferromagnetic to ferromagnetic.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to The American Physical Society.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 03 Jun 2008
Last Modified: 19 Sep 2010 04:45
URI: http://eprints.iisc.ernet.in/id/eprint/14144

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