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

TL;DR

This paper investigates how three-spin and next-nearest neighbor interactions influence the non-equilibrium quenching dynamics of a transverse Ising model, revealing their effects on kink density and critical behavior during quantum phase transitions.

Contribution

It introduces a detailed analysis of the impact of three-spin and NNN interactions on quenching dynamics, including the identification of multicritical points and decay behaviors of kink density.

Findings

Kink density decays as τ^{-1/2} during quenching.

J_3<0.5 increases kink density; J_3>0.5 decreases it.

At J_3=0.5 and h=-0.5, decay slows to τ^{-1/6}.

Abstract

We study the zero temperature quenching dynamics of various extensions of the transverse Ising model (TIM) when the transverse field is linearly quenched from $-\infty$ to $+\infty$ (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 $J_3=0.5$ 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 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.