| We present the zero temperature quenching dynamics of various extensions of the transverse Ising model (TIM) when the transverse field is linearly quenched from -∞ to +∞ (or zero) at a finite and uniform rate. The rate of quenching is dictated by a characteristic scale given by τ. The density of kinks produced in these extended models while crossing the quantum critical points during the quenching process is calculated using a many body generalization of the Landau-Zener transition theory. The density of kinks in the final state is found to decay as τ-1/2. In the first model considered here, the transverse Ising Hamiltonian includes an additional ferromagnetic three spin interaction term of strength J3. For J3 < 0.5, the kink density is found to increase monotonically with J3 whereas it decreases with J3 for J3 > 0.5. The point J3 = 0.5 and the transverse field h = -0.5 is multicritical where the density shows a slower decay given by τ-1/6. We also present a study of the effect of ferromagnetic or antiferromagnetic next nearest neighbor (NNN) interactions on the dynamics of TIM under the same quenching scheme. In a mean field approximation, the transverse Ising Hamiltonians with NNN interactions are identical to the three spin Hamiltonian. The NNN interactions non-trivially modifies the dynamical behavior, for example an antiferromagnetic NNN interactions results to a larger number of kinks in the final state in comparison to the case when the NNN interaction is ferromagnetic. |
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