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Quench dynamics and defect production in the Kitaev and extended Kitaev models

Mondal, Shreyoshi and Sen, Diptiman and Sengupta, K (2008) Quench dynamics and defect production in the Kitaev and extended Kitaev models. In: Physical Review B: Condensed Matter and Materials Physics, 78 (4).

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Official URL: http://prb.aps.org/abstract/PRB/v78/i4/e045101

Abstract

We study quench dynamics and defect production in the Kitaev and the extended Kitaev models. For the Kitaev model in one dimension, we show that in the limit of slow quench rate, the defect density n∼1/√τ, where 1/τ is the quench rate. We also compute the defect correlation function by providing an exact calculation of all independent nonzero spin correlation functions of the model. In two dimensions, where the quench dynamics takes the system across a critical line, we elaborate on the results of earlier work [K. Sengupta, D. Sen, and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008)] to discuss the unconventional scaling of the defect density with the quench rate. In this context, we outline a general proof that for a d-dimensional quantum model, where the quench takes the system through a d−m dimensional gapless (critical) surface characterized by correlation length exponent ν and dynamical critical exponent z, the defect density n∼1/τmν/(zν+1). We also discuss the variation of the shape and spatial extent of the defect correlation function with both the rate of quench and the model parameters and compute the entropy generated during such a quenching process. Finally, we study the defect scaling law, entropy generation and defect correlation function of the two-dimensional extended Kitaev model.

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: 30 Mar 2010 07:11
Last Modified: 19 Sep 2010 05:58
URI: http://eprints.iisc.ernet.in/id/eprint/26691

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