Defect production and quench dynamics in three-dimensional Kitaev model
ABSTRACT :
We study quench dynamics of 3D Kitaev model under a linear drive(Jz → Jt/τ) by filling up the lowest negative energy state which results in a 4-state Landau-Zener problem. Exact numerics as well as independent crossing approximation is used to analysis the system. The defect density scales as τ-1 which is determined by the coupling between the relevant states but not the contour for which the spectrum is gap- less. The asymptotic dependence of the defect density on the ratio Jy/Jx(α) and defect correlation is very different than 2d Kitaev model. The entanglement entropy produced in asymptotic limit is studied in Jτ -α plane and is seen to be maximized near Jτ ≈ 1 where the defect correlation is also found to be maximum. It is seen that for a given value of α maximum value of entanglement entropy is produced at higher value of Jτ in comparison to 2D Kitaev model. Also interestingly for 3D Kitaev model, Jτmax monotonically increases as α increases, reaches a broad maxima and then decreases monotonically. This is in contrast to 2D Kitaev model where Jτmax is non-monotonous with respect to α and has a local minima for finite α.