Slow quench dynamics of the Kitaev model: anisotropic critical point and effect of disorder

Abstract

We study the non-equilibrium slow dynamics for the Kitaev model both in the presence and the absence of disorder. For the case without disorder, we demonstrate, via an exact solution, that the model provides an example of a system with an anisotropic critical point and exhibits unusual scaling of defect density $n$ and residual energy $Q$ for a slow linear quench. We provide a general expression for the scaling of $n$ ($Q$) generated during a slow power-law dynamics, characterized by a rate ${\tau }^{-1}$ and exponent $\alpha$, from a gapped phase to an anisotropic quantum critical point in $d$ dimensions, for which the energy gap ${\Delta }_{\vec{k}}\sim k_i^z$ for $m$ momentum components ($i=\mathrm{1..}m$) and $\sim k_i^{z^{\prime }}$ for the rest $d-m$ components ($i=m+\mathrm{1..}d$) with $z\le z^{\prime }$: $n\sim {\tau }^{-[m+(d-m)z/z^{\prime }]\nu \alpha /(z\nu \alpha +1)}$ ($Q\sim {\tau }^{-[(m+z)+(d-m)z/z^{\prime }]\nu \alpha /(z\nu \alpha +1)}$). These general expressions reproduce both the corresponding results for the Kitaev model as a special case for $d=z^{\prime }=2$ and $m=z=\nu =1$ and the well-known scaling laws of $n$ and $Q$ for isotropic critical points for $z=z^{\prime }$. We also present an exact computation of all non-zero, independent, multispin correlation functions of the Kitaev model for such a quench and discuss their spatial dependence. For the disordered Kitaev model, where the disorder is introduced via random choice of the link variables $D_n$ in the model's Fermionic representation, we find that $n\sim {\tau }^{-1/2}$ and $Q\sim {\tau }^{-1}$ ($Q\sim {\tau }^{-1/2}$) for a slow linear quench ending in the gapless (gapped) phase. We provide a qualitative explanation of such scaling.

10 pages, 11 Figs. v1

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• Probing the Superfluid to Mott Insulator Transition at the Single Atom Level
• Universal adiabatic dynamics across a quantum critical point
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• 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
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Defect production in non-linear quench across a quantum critical point
• Exact results for quench dynamics and defect production in a two-dimensional model
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• 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
• Defect generation in a spin-1/2 transverse XY chain under repeated quenching of the transverse field

Cited by in corpus (20)

• Hunting Majorana Fermions in Kitaev Magnets
• Slow quenches in a quantum Ising chain; dynamical phase transitions and topology
• Quenches and dynamical phase transitions in a non-integrable quantum Ising model
• Tuning the presence of dynamical phase transitions in a generalized $XY$ spin chain
• Quench dynamics and parity blocking in Majorana wires
• Topological Blocking in Quantum Quench Dynamics
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• On the thermalization of a Luttinger liquid after a sequence of sudden interaction quenches
• Dynamics of decoherence: universal scaling of the decoherence factor
• An exactly solvable quench protocol for integrable spin models
• Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit
• Nonequilibrium Majorana Dynamics by Quenching a Magnetic Field in Kitaev Spin Liquids
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field
• Sudden quenching in the Kitaev honeycomb model: Study of defect and heat generation
• Universal scaling in quenches across a discontinuity critical point
• Work statistics across a quantum critical surface
• Dynamical manipulation of Dirac points in the Kitaev honeycomb model
• Quenching across quantum critical points in periodic systems: dependence of scaling laws on periodicity
• Half Landau-Zener ramp to a quantum phase transition in a dissipative single spin sodel