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

Abstract

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.

Final version; Accepted for publication in Physical Review Letters

References in corpus (13)

• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Universal adiabatic dynamics across a quantum critical point
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Quench dynamics across quantum critical points
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Exact results for quench dynamics and defect production in a two-dimensional model
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point
• Adiabatic quenches through an extended quantum critical region

Cited by in corpus (11)

• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Optimal non-linear passage through a quantum critical point
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Quenching along a gapless line: A different exponent for defect density
• Defect production due to quenching through a multicritical point
• Theory of defect production in nonlinear quench across a quantum critical point
• Adiabatic nonlinear probes of one-dimensional Bose gases
• Effects of interference in the dynamics of spin-1/2 transverse XY Chain driven periodically through quantum critical points
• Adiabatic dynamics in a spin-1 chain with uniaxial single-spin anisotropy