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arXiv:1812.09923 · Physical review. B./Physical review. B

Defect production and quench dynamics in the three-dimensional Kitaev model

Subhajit Sarkar, Dibyendu Rana, Saptarshi Mandal

Published Oct 21, 2020• 7 citations
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Abstract

We study the quench dynamics of the three-dimensional Kitaev (spin) model under a linear drive using both exact numerical calculations and analytical independent crossing approximation. Unlike the two-dimensional Kitaev model, the three-dimensional Kitaev model reduces to a multilevel Landau-Zener problem for each momentum. We show that for the slow quench, the defect density is proportional to the quench rate $1/\ensuremath{\tau}$. We find that the zeros of the relevant coupling between the levels determine the nonadiabatic condition for the production of defects. The contour on which the energy spectrum becomes gapless does not play an active role. The asymptotic behavior of the defect density crucially depends on the way the system reaches the nonadiabatic regime during the quenching process. We analytically show that defect correlation varies as ${\ensuremath{\tau}}^{\ensuremath{-}1}{e}^{\ensuremath{-}A/\ensuremath{\tau}}$ where $A$ is a constant independent of $\ensuremath{\tau}$. For the slow quench, the qualitative dependence of the entropy (produced during the quenching process) on the quench time is the same as that of the defect correlation, indicating a close connection between the defect correlation and the entropy content of the final state. Possible experimental realization of such quench dynamics is also described briefly.

DOI
10.1103/physrevb.102.134309

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We study the quenching dynamics of a one-dimensional spin-1/2 XYXYXY model in a transverse field when the transverse field $h(=t/\ensuremath{\tau})$ is quenched repeatedly between $\ensuremath{-}\ensuremath{\infty}$ and $+\ensuremath{\infty}$. A single passage from $h\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ to $h\ensuremath{\rightarrow}+\ensuremath{\infty}$ or the other way around is referred to as a half period of quenching. For an even number of half periods, the transverse field is brought back to the initial value of $\ensuremath{-}\ensuremath{\infty}$; in the case of an odd number of half periods, the dynamics is stopped at $h\ensuremath{\rightarrow}+\ensuremath{\infty}$. The density of defects produced due to the nonadiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as $1/\sqrt{\ensuremath{\tau}}$ for large $\ensuremath{\tau}$; however, the magnitude is found to depend on the number of half periods of quenching. For two successive half periods, the defect density is found to decrease in comparison to a single half period, suggesting the existence of a corrective mechanism in the reverse path. A similar behavior of the density of defects and the local entropy is observed for repeated quenching. The defect density decays as $1/\sqrt{\ensuremath{\tau}}$ for large $\ensuremath{\tau}$ for any number of half periods, and shows an increase in kink density for small $\ensuremath{\tau}$ for an even number; the entropy shows qualitatively the same behavior for any number of half periods. The probability of nonadiabatic transitions and the local entropy saturate to 1/2 and ln 2\text{ln}\text{ }2ln 2, respectively, for a large number of repeated quenching.