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.
Ref: Dibyendu Rana, Subhajit Sarkar and Saptarshi Mandal, arXiv:1812.09923