The effect of the three-spin interaction and the next nearest neighbor interaction on the quenching dynamics of a transverse Ising model

We study the zero-temperature quenching dynamics of various extensions of the transverse Ising model (TIM) for when the transverse field is linearly quenched from - infinity to + infinity (or zero) at a finite and uniform rate. The rate of quenching is dictated by a characteristic scale given by tau. 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 tau(-1/2). In the first model considered here, the transverse Ising Hamiltonian includes an additional ferromagnetic three-spin interaction term of strength J(3). For J(3) < 0.5, the kink density is found to increase monotonically with J(3) whereas it decreases with J(3) for J(3) < 0.5. The point with J(3) = 0.5 and the transverse field h = -0.5 is multicritical, where the density shows a slower decay given by tau(-1/6). We also study the effect of ferromagnetic or antiferromagnetic next nearest neighbor (NNN) interactions on the dynamics of the 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 modify the dynamical behavior; for example an antiferromagnetic NNN interaction results in a larger number of kinks in the final state in comparison to the case when the NNN interaction is ferromagnetic.