Quenching along a gapless line: A different exponent for defect density

TL;DR

This paper investigates a novel quenching scheme in a one-dimensional anisotropic XY spin chain, revealing a unique defect density scaling of 1/τ^{1/3} when crossing a gapless phase, and proposes a general scaling law.

Contribution

The study introduces a new quenching protocol along a gapless line and derives a distinct defect density scaling law, expanding understanding of non-equilibrium dynamics in quantum critical systems.

Findings

Defect density scales as 1/τ^{1/3} when quenching along a gapless line.

Mapping to Landau-Zener problem enables analytical derivation of defect scaling.

Generalized model confirms the universality of the scaling law.

Abstract

We use a new 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 $h+\de$ and $h-\de$ from site to site. In this quenching scheme, the parameter denoting the anisotropy of interaction ($\ga$) is linearly quenched from $-\infty$ to $ +\infty$ as $\ga = t/\tau$, keeping the total strength of interaction $J$ fixed. The system traverses through a gapless phase when $\ga$ is quenched along the critical surface $h^2 = \de^2 + J^2$ in the parameter space spanned by $h$, $\de$ and $\ga$. 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.