We use a quenching scheme to study the dynamics of a one-dimensional anisotropic $XY$ spin-1/2 chain in the presence of a transverse field which alternates between the values $h+\delta$ and $h-\delta$ from site to site. In this quenching scheme, the parameter denoting the anisotropy of interaction $\left(\gamma \right)$ is linearly quenched from $-\infty$ to $+\infty$ as $\gamma =t/\tau$, keeping the total strength of interaction $J$ fixed. The system traverses through a gapless phase when $\gamma$ is quenched along the critical surface $h^2={\delta }^2+J^2$ in the parameter space spanned by $h$, $\delta$, and $\gamma$. By mapping to an equivalent two-level Landau-Zener problem, we show that the defect density in the final state scales as $1/{\tau }^{1/3}$, a behavior that has not been observed in previous studies of quenching through a gapless phase. We also generalize the model incorporating additional alternations in the anisotropy or in the strength of the interaction and derive an identical result under a similar quenching. Based on the above results, we propose a general scaling of the defect density with the quenching rate $\tau$ for quenching along a gapless critical line.

• Received 27 May 2008

DOI:https://doi.org/10.1103/PhysRevB.78.144301