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

Abstract

We study the zero-temperature quenching dynamics of various extensions of the transverseIsing model (TIM) for 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 givenby τ. The density of kinks produced in these extended models while crossing the quantum criticalpoints during the quenching process is calculated using a many-body generalization of theLandau–Zener transition theory. The density of kinks in the final state is found to decay asτ−1/2. In the first model considered here, the transverse Ising Hamiltonianincludes an additional ferromagnetic three-spin interaction term of strengthJ3.For J3<0.5, the kink density is found to increase monotonically withJ3 whereas itdecreases with J3 for J3>0.5. The pointwith J3 = 0.5 and thetransverse field h = −0.5 is multicritical, where the density shows a slower decay given byτ−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 amean field approximation, the transverse Ising Hamiltonians with NNN interactions areidentical to the three-spin Hamiltonian. The NNN interactions non-trivially modify thedynamical behavior; for example an antiferromagnetic NNN interaction results in a largernumber of kinks in the final state in comparison to the case when the NNN interaction isferromagnetic.