Exact results for quench dynamics and defect production in a two-dimensional model

Abstract

We show that for a d-dimensional model in which a quench with a rate τ^{-1} takes the system across a d-m dimensional critical surface, the defect density scales as n \sim 1/τ^{mν/(zν+1)}, where νand z are the correlation length and dynamical critical exponents characterizing the critical surface. We explicitly demonstrate that the Kitaev model provides an example of such a scaling with d=2 and m=ν=z=1. We also provide the first example of an exact calculation of some multispin correlation functions for a two-dimensional model which can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.

4 pages including 4 figures; generalized the discussion of the defect density scaling to the case of arbitrary critical exponents, and added some references; this version will appear in Physical Review Letters

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• Universal adiabatic dynamics across a quantum critical point
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Quench dynamics across quantum critical points
• Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
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• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Non-adiabacity and large flucutations in a many particle Landau Zener problem
• Quenching along a gapless line: A different exponent for defect density
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Defect production due to quenching through a multicritical point
• Theory of defect production in nonlinear quench across a quantum critical point
• Adiabatic quenches through an extended quantum critical region
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• Defect generation in a spin-1/2 transverse XY chain under repeated quenching of the transverse field
• Effects of interference in the dynamics of spin-1/2 transverse XY Chain driven periodically through quantum critical points
• Exact results for the criticality of quench dynamics in quantum Ising models
• Adiabatic dynamics in a spin-1 chain with uniaxial single-spin anisotropy