Defect production in non-linear quench across a quantum critical point

Details Defect production in non-linear quench across a quantum critical point Defect production in non-linear quench across a quantum critical point

2008-03-14

arxiv.org/abs/0803.2081v2

Phys. Rev. Lett. 101, 016806 (2008)

Physics

Condensed Matter

Strongly Correlated Electrons

Final version; Accepted for publication in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.101.016806

We show that the defect density $n$, for a slow non-linear power-law quench with a rate $\tau^{-1}$ and an exponent $\alpha>0$, which takes the system through a critical point characterized by correlation length and dynamical critical exponents $\nu$ and $z$, scales as $n \sim \tau^{-\alpha \nu d/ (\alpha z\nu+1)}$ [$n \sim (\alpha g^{(\alpha-1)/\alpha}/\tau)^{\nu d/(z\nu+1)}$], if the quench takes the system across the critical point at time $t=0$ [$t=t_0 \ne 0$], where $g$ is a non-universal constant and $d$ is the system dimension. These scaling laws constitute the first theoretical results for defect production in non-linear quenches across quantum critical points and reproduce their well-known counterpart for linear quench ($\alpha=1$) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.

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